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Gruber, Peter Manfred(b. 1941 d. 2017)

Author ID:	gruber.peter-manfred
Published as:	Gruber, Peter M.;Gruber, P. M.;Gruber, Peter;Gruber, P.;Gruber, Peter Manfredmore...less
Homepage:	https://dmg.tuwien.ac.at/gruber/
External Links:	MGP ·Wikidata ·Google Scholar ·Math-Net.Ru ·dblp ·GND ·IdRef

Documents Indexed:	114 Publications since 1967, including4 Books
	10 Contributions as Editor ·1 Further Contribution
Reviewing Activity:	127 Reviews
Biographic References:	2 Publications
Co-Authors:	38 Co-Authors with 34 Joint Publications
	1,338 Co-Co-Authors

all top 5

Co-Authors

90	single-authored
4	Hlawka, Edmund
3	Aliev, Iskander M.
3	Schmidt, Wolfgang M.
3	Wills, Jörg M.
2	Lekkerkerker, Cornelis Gerrit
2	Lettl, Günter Hermann Alexander
2	Schmetterer, Leopold
2	Tichy, Robert Franz
1	Aigner, Martin
1	Balasubramanian, Ramachandran
1	Ball, Keith Martin
1	Bayoumi, Mohamed M.
1	Bianchi, Gabriele
1	Dani, Shrikrishna Gopalrao
1	Drmota, Michael
1	Erdős, Pál
1	Flor, Peter
1	Glasauer, Stefan
1	Goodey, Paul R.
1	Hammer, Joseph
1	Hans-Gill, Rajinder J.
1	Helmberg, Gilbert
1	Höbinger, Johannes
1	Kenderov, Petar Stojanov
1	Ludwig, Monika
1	Menger, Karl
1	Nöbauer, Wilfried
1	Ódor, Tibor
1	Radon, Johann
1	Ramharter, Gerhard
1	Reich, Ludwig
1	Ryshkov, Sergeĭ Sergeevich
1	Schneider, Rolf G.
1	Schoißengeier, Johannes
1	Schuster, Franz E.
1	Schweizer, Berthold
1	Sigmund, Karl
1	Sklar, Abe
1	Sorger, Hartwig
1	Theis, Fabian Joachim
1	Winkler, Reinhard
1	Zamfirescu, Tudor I.

all top 5

Serials

6	Archiv der Mathematik
6	Monatshefte für Mathematik
5	Mathematische Annalen
5	Discrete & Computational Geometry
5	Forum Mathematicum
4	Geometriae Dedicata
4	Journal für die Reine und Angewandte Mathematik
3	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3	Advances in Mathematics
2	Acta Arithmetica
2	Annali di Matematica Pura ed Applicata. Serie Quarta
2	Journal of Number Theory
2	Mathematika
2	Rendiconti del Circolo Matemàtico di Palermo. Serie II
2	Studia Scientiarum Mathematicarum Hungarica
2	Internationale Mathematische Nachrichten
2	Rendiconti del Seminario Matematico di Messina. Serie II
2	Advances in Geometry
2	Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse. Sitzungsberichte. Abteilung II
2	Proceedings of the Steklov Institute of Mathematics
2	Supplemento ai Rendiconti del Circolo Matemàtico di Palermo. Serie II
1	Acta Mathematica Academiae Scientiarum Hungaricae
1	Israel Journal of Mathematics
1	Mathematische Semesterberichte
1	Mitteilungen der Deutschen Mathematiker-Vereinigung (DMV)
1	The Mathematical Intelligencer
1	Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica
1	Bulletin of the London Mathematical Society
1	Colloquium Mathematicum
1	IEEE Transactions on Automatic Control
1	Journal of the London Mathematical Society. Second Series
1	Manuscripta Mathematica
1	Sitzungsberichte. Abteilung II. Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse
1	Proceedings of the American Mathematical Society
1	Transactions of the American Mathematical Society
1	Rendiconti del Seminario Matematico
1	European Journal of Combinatorics
1	Potsdamer Forschungen. Wissenschaftliche Schriftenreihe der Pädagogischen Hochschule ”Karl Liebknecht” Potsdam. Reihe B. Naturwissenschaftliche Reihe
1	Aequationes Mathematicae
1	Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali
1	Doklady Bolgarskoĭ Akademii Nauk
1	Elemente der Mathematik
1	Expositiones Mathematicae
1	Oberwolfach Reports
1	Bollettino della Unione Matematica Italiana. Series IV
1	Contributions to Discrete Mathematics
1	Grundlehren der Mathematischen Wissenschaften
1	North-Holland Mathematical Library
1	Pitman Monographs and Surveys in Pure and Applied Mathematics
1	Ramanujan Mathematical Society Lecture Notes Series
1	Springer Collected Works in Mathematics

all top 5

Fields

102	Convex and discrete geometry (52-XX)
35	Number theory (11-XX)
17	Differential geometry (53-XX)
9	Approximations and expansions (41-XX)
9	Functional analysis (46-XX)
8	History and biography (01-XX)
8	Combinatorics (05-XX)
8	General topology (54-XX)
7	General and overarching topics; collections (00-XX)
6	Numerical analysis (65-XX)
5	Probability theory and stochastic processes (60-XX)
4	Measure and integration (28-XX)
4	Geometry (51-XX)
3	Operator theory (47-XX)
3	Information and communication theory, circuits (94-XX)
2	Linear and multilinear algebra; matrix theory (15-XX)
2	Topological groups, Lie groups (22-XX)
2	Real functions (26-XX)
2	Dynamical systems and ergodic theory (37-XX)
1	Order, lattices, ordered algebraic structures (06-XX)
1	Algebraic geometry (14-XX)
1	Functions of a complex variable (30-XX)
1	Special functions (33-XX)
1	Difference and functional equations (39-XX)
1	Calculus of variations and optimal control; optimization (49-XX)
1	Manifolds and cell complexes (57-XX)
1	Global analysis, analysis on manifolds (58-XX)
1	Computer science (68-XX)
1	Geophysics (86-XX)
1	Operations research, mathematical programming (90-XX)
1	Biology and other natural sciences (92-XX)
1	Systems theory; control (93-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

99 Publications have been cited 1,800 times in1,355 Documents	Cited by ▼	Year ▼
Convex and discrete geometry. Zbl 1139.52001 Gruber, Peter M.	443	2007
Geometry of numbers. 2nd ed. Zbl 0611.10017 Gruber, P. M.;Lekkerkerker, C. G.	282	1987
Stability of isometries. Zbl 0393.41020 Gruber, Peter M.	86	1978
Aspects of approximation of convex bodies. Zbl 0791.52007 Gruber, Peter M.	73	1993
Handbook of convex geometry. Volume A. Zbl 0777.52001	63	1993
Optimum quantization and its applications. Zbl 1062.94012 Gruber, Peter M.	43	2004
An arithmetic proof of John’s ellipsoid theorem. Zbl 1086.52002 Gruber, Peter M.;Schuster, Franz E.	38	2005
Lattice points. Zbl 0683.10025 Erdős, Paul;Gruber, P. M.;Hammer, J.	37	1989
Asymptotic estimates for best and stepwise approximation of convex bodies. II. Zbl 0788.41020 Gruber, Peter M.	35	1993
Baire categories in convexity. Zbl 0791.52002 Gruber, Peter M.	30	1993
Approximation of convex bodies. Zbl 0519.52005 Gruber, Peter M.	25	1983
Handbook of convex geometry. Volume B. Zbl 0777.52002	24	1993
Minimal ellipsoids and their duals. Zbl 0673.52002 Gruber, Peter M.	22	1988
John and Loewner ellipsoids. Zbl 1241.52002 Gruber, Peter M.	21	2011
Convexity and its applications. Zbl 0512.00020	21	1983
Asymptotic estimates for best and stepwise approximation of convex bodies. III. Zbl 0889.52006 Glasauer, Stefan;Gruber, Peter M.	21	1997
Asymptotic estimates for best and stepwise approximation of convex bodies. I. Zbl 0780.52005 Gruber, Peter M.	20	1993
Comparisons of best and random approximation of convex bodies by polytopes. Zbl 0896.52014 Gruber, Peter M.	20	1997
Dimension and structure of typical compact sets, continua and curves. Zbl 0666.28005 Gruber, P. M.	17	1989
Volume approximation of convex bodies by inscribed polytopes. Zbl 0628.52006 Gruber, Peter M.	16	1988
The endomorphisms of the lattice of norms in finite dimensions. Zbl 0779.52006 Gruber, P. M.	15	1992
In most cases approximation is irregular. Zbl 0562.41030 Gruber, Peter M.	15	1983
Problems in geometric convexity. Zbl 0433.52001 Gruber, P. M.;Schneider, R.	14	1979
The space of convex bodies. Zbl 0791.52004 Gruber, Peter M.	14	1993
Approximation of convex bodies by polytopes. Zbl 0494.52003 Gruber, Peter M.;Kenderov, Petar	14	1982
Application of an idea of Voronoĭ to John type problems. Zbl 1144.52003 Gruber, Peter M.	14	2008
An optimal lower bound for the Frobenius problem. Zbl 1114.11025 Aliev, Iskander M.;Gruber, Peter M.	14	2007
Die meisten konvexen Körper sind glatt, aber nicht zu glatt. Zbl 0342.52009 Gruber, Peter M.	13	1977
Approximation of convex bodies by polytopes. Zbl 0474.52007 Gruber, P. M.	13	1981
Fixpunktmengen von Kontraktionen in endlichdimensionalen normierten Räumen. Zbl 0318.47031 Gruber, Peter M.	12	1975
The endomorphisms of the lattice of convex bodies. Zbl 0754.52006 Gruber, P. M.	11	1991
Results of Baire category type in convexity. Zbl 0571.52007 Gruber, Peter M.	11	1985
Only ellipsoids have caustics. Zbl 0847.34052 Gruber, Peter M.	11	1995
Characterizations of ellipsoids. Zbl 0595.52004 Bianchi, Gabriele;Gruber, Peter M.	11	1987
Isometries of the space of convex bodies in Euclidean space. Zbl 0447.52004 Gruber, Peter M.;Lettl, Günter	11	1980
Application of an idea of Voronoĭ to lattice zeta functions. Zbl 1297.11113 Gruber, Peter M.	11	2012
Volume approximation of convex bodies by circumscribed polytopes. Zbl 0739.52004 Gruber, Peter M.	10	1991
Approximation by convex polytopes. Zbl 0824.52007 Gruber, P. M.	10	1994
A typical convex surface contains no closed geodesic. Zbl 0718.52003 Gruber, Peter M.	9	1991
Generic properties of compact starshaped sets. Zbl 0683.52008 Gruber, Peter M.;Zamfirescu, Tudor I.	9	1990
Convex billiards. Zbl 0696.52001 Gruber, Peter M.	8	1990
A short analytic proof of Fejes Tóth’s theorem on sums of moments. Zbl 1006.52015 Gruber, Peter M.	8	1999
Error of asymptotic formulae for volume approximation of convex bodies in \({\mathbb E}^d\). Zbl 1006.52002 Gruber, Peter M.	7	2002
Optimal configurations of finite sets in Riemannian 2-manifolds. Zbl 0982.52020 Gruber, Peter M.	7	2001
Geometry of the cone of positive quadratic forms. Zbl 1217.11039 Gruber, Peter M.	7	2009
Expectation of random polytopes. Zbl 0873.52006 Gruber, Peter M.	7	1996
Geometry of numbers. Zbl 0788.11022 Gruber, Peter M.	6	1993
Über kennzeichnende Eigenschaften von euklidischen Räumen. und Ellipsoiden. I. Zbl 0273.52001 Gruber, Peter	6	1974
Zur Charakterisierung konvexer Körper. Über einen Satz von Rogers und Shephard. II. Zbl 0175.49101 Gruber, P.	6	1970
Isometries of the space of convex bodies of \(E^4\). Zbl 0403.52002 Gruber, Peter M.	6	1979
Über kennzeichnende Eigenschaften von euklidischen Räumen und Ellipsoiden. II. Zbl 0291.52004 Gruber, Peter	6	1974
Kennzeichnungen von Ellipsoiden mit Anwendungen. Zbl 0325.52006 Gruber, Peter M.;Höbinger, Johannes	6	1976
Uniqueness of lattice packings and coverings of extreme density. Zbl 1230.52030 Gruber, Peter M.	5	2011
Typical convex bodies have surprisingly few neighbours in densest lattice packings. Zbl 0545.52008 Gruber, Peter M.	5	1986
Isometries of the space of compact subsets of \(E^ n\). Zbl 0484.52011 Gruber, Peter M.;Lettl, Guenter	5	1979
History of convexity. Zbl 0791.52001 Gruber, Peter M.	5	1993
Ellipsoids are the most symmetric convex bodies. Zbl 0942.52001 Gruber, Peter M.;Ódor, Tibor	5	1999
Eine Erweiterung des Blichfeldtschen Satzes mit einer Anwendung auf inhomogene Linearformen. Zbl 0171.01003 Gruber, P.	5	1967
A Helmholtz-Lie type characterization of ellipsoids. II. Zbl 0864.52005 Gruber, P. M.;Ludwig, M.	5	1996
Über kennzeichnende Eigenschaften von Ellipsoiden und euklidischen Räumen. III. Zbl 0291.52005 Gruber, P.	5	1974
Kontrahierende Radialprojektionen in normierten Räumen. Zbl 0338.47029 Gruber, Peter	5	1975
Voronoĭ type criteria for lattice coverings with balls. Zbl 1238.05051 Gruber, Peter M.	4	2011
Collected works. Volumes 1, 2. Ed. by Peter Manfred Gruber, Edmund Hlawka, Wilfried Nöbauer, Leopold Schmetterer. Zbl 0626.01038 Radon, Johann	4	1987
Planar Chebyshev sets. Zbl 0591.52003 Gruber, P. M.	4	1984
In many cases optimal configurations are almost regular hexagonal. Zbl 1017.11032 Gruber, Peter M.	4	2000
Zur Charakterisierung konvexer Körper: Über einen Satz von Rogers und Shephard. Zbl 0159.51702 Gruber, P.	4	1969
Asymptotic estimates for best and stepwise approximation of convex bodies. IV. Zbl 0927.52009 Gruber, Peter M.	4	1998
Eine Bemerkung über DOTU-Matrizen. Zbl 0331.10016 Gruber, Peter	4	1976
Über die Durchschnitte von translationsgleichen Polyedern. Zbl 0195.51701 Gruber, Peter	4	1970
Suboptimal control strategies for multilocomotive powered trains. Zbl 0478.93010 Gruber, Peter;Bayoumi, Mohamed M.	4	1982
Optimal quantization. (Optimale Quantisierung.) Zbl 1032.52001 Gruber, Peter M.	3	2002
Selecta Mathematica. Vol. 1. Zbl 1027.01021 Menger, Karl	3	2002
Beiträge zum Umkehrproblem für den Minkowskischen Linearformensatz. Zbl 0488.10028 Gruber, P. M.;Ramharter, G.	3	1982
Optimal arrangement of finite point sets in Riemannian 2-manifolds. Zbl 0982.52021 Gruber, P. M.	3	1999
Stability of Blaschke’s characterization of ellipsoids and Radon norms. Zbl 0887.52002 Gruber, P. M.	3	1997
Über einen Satz von Remak in der Geometrie der Zahlen. Zbl 0207.35601 Gruber, Peter	3	1970
Bemerkungen zum Umkehrproblem für den Minkowskischen Linearformensatz. Zbl 0213.05902 Gruber, P.	3	1971
Application of an idea of Voronoĭ to lattice packing. Zbl 1297.05047 Gruber, Peter M.	3	2014
Lattice points in large Borel sets and successive minima. Zbl 1215.11066 Aliev, Iskander;Gruber, Peter M.	3	2006
Lattice packing and covering of convex bodies. Zbl 1301.52033 Gruber, Peter M.	3	2011
Isometries of the space of convex bodies contained in a Euclidean ball. Zbl 0502.52006 Gruber, Peter M.	2	1982
On the history of convex geometry and the geometry of numbers. (Zur Geschichte der Konvexgeometrie und der Geometrie der Zahlen.) Zbl 0864.11004 Gruber, Peter Manfred	2	1990
Error of asymptotic formulae for volume approximation of convex bodies in \(E^3\). Zbl 1068.52007 Gruber, P. M.	2	2002
A Helmholtz-Lie type characterization of ellipsoids. I. Zbl 0824.52006 Gruber, P. M.	2	1995
Facet-to-facet implies face-to-face. Zbl 0664.52011 Gruber, Peter M.;Ryshkov, Sergej S.	2	1989
Normal bundles of convex bodies. Zbl 1296.52003 Gruber, Peter M.	2	2014
The space of compact subsets of \(E^d\). Zbl 0432.54008 Gruber, Peter M.	2	1980
Isometries of spaces of compact or compact convex subsets of metric manifolds. Zbl 0449.52001 Gruber, P. M.;Tichy, R.	2	1982
Aspects of convexity and its applications. Zbl 0525.52001 Gruber, Peter M.	2	1984
Geodesics on typical convex surfaces. Zbl 0741.52006 Gruber, Peter Manfred	1	1988
Shadow boundaries of typical convex bodies. Measure properties. Zbl 0667.52002 Gruber, Peter M.;Sorger, Hartwig	1	1989
On the product of inhomogeneous linear forms. (Über das Produkt inhomogener Linearformen.) Zbl 0153.07102 Gruber, Peter	1	1967
Zur Gitterüberdeckung des \(R^ n\) durch Sternkörper. Zbl 0164.05305 Gruber, P.	1	1968
Über eine Kennzeichnung der Simplices des \(R^ n\). Zbl 0215.50701 Gruber, P.	1	1971
Über den Durchschnitt einer abnehmenden Folge von Parallelepipeden. Zbl 0342.52012 Gruber, Peter M.	1	1977
Geometry of numbers. Zbl 0425.10035 Gruber, Peter M.	1	1979
Isometrien des Konvexringes. Zbl 0462.52003 Gruber, Peter M.	1	1980
Best simultaneous Diophantine approximations under a constraint on the denominator. Zbl 1139.11031 Aliev, Iskander;Gruber, Peter	1	2006
Applications of an idea of Voronoĭ, a report. Zbl 1317.15023 Gruber, Peter M.	1	2013
Application of an idea of Voronoĭ to lattice packing. Zbl 1297.05047 Gruber, Peter M.	3	2014
Normal bundles of convex bodies. Zbl 1296.52003 Gruber, Peter M.	2	2014
Applications of an idea of Voronoĭ, a report. Zbl 1317.15023 Gruber, Peter M.	1	2013
Application of an idea of Voronoĭ to lattice zeta functions. Zbl 1297.11113 Gruber, Peter M.	11	2012
John and Loewner ellipsoids. Zbl 1241.52002 Gruber, Peter M.	21	2011
Uniqueness of lattice packings and coverings of extreme density. Zbl 1230.52030 Gruber, Peter M.	5	2011
Voronoĭ type criteria for lattice coverings with balls. Zbl 1238.05051 Gruber, Peter M.	4	2011
Lattice packing and covering of convex bodies. Zbl 1301.52033 Gruber, Peter M.	3	2011
Geometry of the cone of positive quadratic forms. Zbl 1217.11039 Gruber, Peter M.	7	2009
Application of an idea of Voronoĭ to John type problems. Zbl 1144.52003 Gruber, Peter M.	14	2008
Convex and discrete geometry. Zbl 1139.52001 Gruber, Peter M.	443	2007
An optimal lower bound for the Frobenius problem. Zbl 1114.11025 Aliev, Iskander M.;Gruber, Peter M.	14	2007
Lattice points in large Borel sets and successive minima. Zbl 1215.11066 Aliev, Iskander;Gruber, Peter M.	3	2006
Best simultaneous Diophantine approximations under a constraint on the denominator. Zbl 1139.11031 Aliev, Iskander;Gruber, Peter	1	2006
An arithmetic proof of John’s ellipsoid theorem. Zbl 1086.52002 Gruber, Peter M.;Schuster, Franz E.	38	2005
Optimum quantization and its applications. Zbl 1062.94012 Gruber, Peter M.	43	2004
Error of asymptotic formulae for volume approximation of convex bodies in \({\mathbb E}^d\). Zbl 1006.52002 Gruber, Peter M.	7	2002
Optimal quantization. (Optimale Quantisierung.) Zbl 1032.52001 Gruber, Peter M.	3	2002
Selecta Mathematica. Vol. 1. Zbl 1027.01021 Menger, Karl	3	2002
Error of asymptotic formulae for volume approximation of convex bodies in \(E^3\). Zbl 1068.52007 Gruber, P. M.	2	2002
Optimal configurations of finite sets in Riemannian 2-manifolds. Zbl 0982.52020 Gruber, Peter M.	7	2001
In many cases optimal configurations are almost regular hexagonal. Zbl 1017.11032 Gruber, Peter M.	4	2000
A short analytic proof of Fejes Tóth’s theorem on sums of moments. Zbl 1006.52015 Gruber, Peter M.	8	1999
Ellipsoids are the most symmetric convex bodies. Zbl 0942.52001 Gruber, Peter M.;Ódor, Tibor	5	1999
Optimal arrangement of finite point sets in Riemannian 2-manifolds. Zbl 0982.52021 Gruber, P. M.	3	1999
Asymptotic estimates for best and stepwise approximation of convex bodies. IV. Zbl 0927.52009 Gruber, Peter M.	4	1998
Asymptotic estimates for best and stepwise approximation of convex bodies. III. Zbl 0889.52006 Glasauer, Stefan;Gruber, Peter M.	21	1997
Comparisons of best and random approximation of convex bodies by polytopes. Zbl 0896.52014 Gruber, Peter M.	20	1997
Stability of Blaschke’s characterization of ellipsoids and Radon norms. Zbl 0887.52002 Gruber, P. M.	3	1997
Expectation of random polytopes. Zbl 0873.52006 Gruber, Peter M.	7	1996
A Helmholtz-Lie type characterization of ellipsoids. II. Zbl 0864.52005 Gruber, P. M.;Ludwig, M.	5	1996
Only ellipsoids have caustics. Zbl 0847.34052 Gruber, Peter M.	11	1995
A Helmholtz-Lie type characterization of ellipsoids. I. Zbl 0824.52006 Gruber, P. M.	2	1995
Approximation by convex polytopes. Zbl 0824.52007 Gruber, P. M.	10	1994
Aspects of approximation of convex bodies. Zbl 0791.52007 Gruber, Peter M.	73	1993
Handbook of convex geometry. Volume A. Zbl 0777.52001	63	1993
Asymptotic estimates for best and stepwise approximation of convex bodies. II. Zbl 0788.41020 Gruber, Peter M.	35	1993
Baire categories in convexity. Zbl 0791.52002 Gruber, Peter M.	30	1993
Handbook of convex geometry. Volume B. Zbl 0777.52002	24	1993
Asymptotic estimates for best and stepwise approximation of convex bodies. I. Zbl 0780.52005 Gruber, Peter M.	20	1993
The space of convex bodies. Zbl 0791.52004 Gruber, Peter M.	14	1993
Geometry of numbers. Zbl 0788.11022 Gruber, Peter M.	6	1993
History of convexity. Zbl 0791.52001 Gruber, Peter M.	5	1993
The endomorphisms of the lattice of norms in finite dimensions. Zbl 0779.52006 Gruber, P. M.	15	1992
The endomorphisms of the lattice of convex bodies. Zbl 0754.52006 Gruber, P. M.	11	1991
Volume approximation of convex bodies by circumscribed polytopes. Zbl 0739.52004 Gruber, Peter M.	10	1991
A typical convex surface contains no closed geodesic. Zbl 0718.52003 Gruber, Peter M.	9	1991
Generic properties of compact starshaped sets. Zbl 0683.52008 Gruber, Peter M.;Zamfirescu, Tudor I.	9	1990
Convex billiards. Zbl 0696.52001 Gruber, Peter M.	8	1990
On the history of convex geometry and the geometry of numbers. (Zur Geschichte der Konvexgeometrie und der Geometrie der Zahlen.) Zbl 0864.11004 Gruber, Peter Manfred	2	1990
Lattice points. Zbl 0683.10025 Erdős, Paul;Gruber, P. M.;Hammer, J.	37	1989
Dimension and structure of typical compact sets, continua and curves. Zbl 0666.28005 Gruber, P. M.	17	1989
Facet-to-facet implies face-to-face. Zbl 0664.52011 Gruber, Peter M.;Ryshkov, Sergej S.	2	1989
Shadow boundaries of typical convex bodies. Measure properties. Zbl 0667.52002 Gruber, Peter M.;Sorger, Hartwig	1	1989
Minimal ellipsoids and their duals. Zbl 0673.52002 Gruber, Peter M.	22	1988
Volume approximation of convex bodies by inscribed polytopes. Zbl 0628.52006 Gruber, Peter M.	16	1988
Geodesics on typical convex surfaces. Zbl 0741.52006 Gruber, Peter Manfred	1	1988
Geometry of numbers. 2nd ed. Zbl 0611.10017 Gruber, P. M.;Lekkerkerker, C. G.	282	1987
Characterizations of ellipsoids. Zbl 0595.52004 Bianchi, Gabriele;Gruber, Peter M.	11	1987
Collected works. Volumes 1, 2. Ed. by Peter Manfred Gruber, Edmund Hlawka, Wilfried Nöbauer, Leopold Schmetterer. Zbl 0626.01038 Radon, Johann	4	1987
Typical convex bodies have surprisingly few neighbours in densest lattice packings. Zbl 0545.52008 Gruber, Peter M.	5	1986
Results of Baire category type in convexity. Zbl 0571.52007 Gruber, Peter M.	11	1985
Planar Chebyshev sets. Zbl 0591.52003 Gruber, P. M.	4	1984
Aspects of convexity and its applications. Zbl 0525.52001 Gruber, Peter M.	2	1984
Approximation of convex bodies. Zbl 0519.52005 Gruber, Peter M.	25	1983
Convexity and its applications. Zbl 0512.00020	21	1983
In most cases approximation is irregular. Zbl 0562.41030 Gruber, Peter M.	15	1983
Approximation of convex bodies by polytopes. Zbl 0494.52003 Gruber, Peter M.;Kenderov, Petar	14	1982
Suboptimal control strategies for multilocomotive powered trains. Zbl 0478.93010 Gruber, Peter;Bayoumi, Mohamed M.	4	1982
Beiträge zum Umkehrproblem für den Minkowskischen Linearformensatz. Zbl 0488.10028 Gruber, P. M.;Ramharter, G.	3	1982
Isometries of the space of convex bodies contained in a Euclidean ball. Zbl 0502.52006 Gruber, Peter M.	2	1982
Isometries of spaces of compact or compact convex subsets of metric manifolds. Zbl 0449.52001 Gruber, P. M.;Tichy, R.	2	1982
Approximation of convex bodies by polytopes. Zbl 0474.52007 Gruber, P. M.	13	1981
Isometries of the space of convex bodies in Euclidean space. Zbl 0447.52004 Gruber, Peter M.;Lettl, Günter	11	1980
The space of compact subsets of \(E^d\). Zbl 0432.54008 Gruber, Peter M.	2	1980
Isometrien des Konvexringes. Zbl 0462.52003 Gruber, Peter M.	1	1980
Problems in geometric convexity. Zbl 0433.52001 Gruber, P. M.;Schneider, R.	14	1979
Isometries of the space of convex bodies of \(E^4\). Zbl 0403.52002 Gruber, Peter M.	6	1979
Isometries of the space of compact subsets of \(E^ n\). Zbl 0484.52011 Gruber, Peter M.;Lettl, Guenter	5	1979
Geometry of numbers. Zbl 0425.10035 Gruber, Peter M.	1	1979
Stability of isometries. Zbl 0393.41020 Gruber, Peter M.	86	1978
Die meisten konvexen Körper sind glatt, aber nicht zu glatt. Zbl 0342.52009 Gruber, Peter M.	13	1977
Über den Durchschnitt einer abnehmenden Folge von Parallelepipeden. Zbl 0342.52012 Gruber, Peter M.	1	1977
Kennzeichnungen von Ellipsoiden mit Anwendungen. Zbl 0325.52006 Gruber, Peter M.;Höbinger, Johannes	6	1976
Eine Bemerkung über DOTU-Matrizen. Zbl 0331.10016 Gruber, Peter	4	1976
Fixpunktmengen von Kontraktionen in endlichdimensionalen normierten Räumen. Zbl 0318.47031 Gruber, Peter M.	12	1975
Kontrahierende Radialprojektionen in normierten Räumen. Zbl 0338.47029 Gruber, Peter	5	1975
Über kennzeichnende Eigenschaften von euklidischen Räumen. und Ellipsoiden. I. Zbl 0273.52001 Gruber, Peter	6	1974
Über kennzeichnende Eigenschaften von euklidischen Räumen und Ellipsoiden. II. Zbl 0291.52004 Gruber, Peter	6	1974
Über kennzeichnende Eigenschaften von Ellipsoiden und euklidischen Räumen. III. Zbl 0291.52005 Gruber, P.	5	1974
Bemerkungen zum Umkehrproblem für den Minkowskischen Linearformensatz. Zbl 0213.05902 Gruber, P.	3	1971
Über eine Kennzeichnung der Simplices des \(R^ n\). Zbl 0215.50701 Gruber, P.	1	1971
Zur Charakterisierung konvexer Körper. Über einen Satz von Rogers und Shephard. II. Zbl 0175.49101 Gruber, P.	6	1970
Über die Durchschnitte von translationsgleichen Polyedern. Zbl 0195.51701 Gruber, Peter	4	1970
Über einen Satz von Remak in der Geometrie der Zahlen. Zbl 0207.35601 Gruber, Peter	3	1970
Zur Charakterisierung konvexer Körper: Über einen Satz von Rogers und Shephard. Zbl 0159.51702 Gruber, P.	4	1969
Zur Gitterüberdeckung des \(R^ n\) durch Sternkörper. Zbl 0164.05305 Gruber, P.	1	1968
Eine Erweiterung des Blichfeldtschen Satzes mit einer Anwendung auf inhomogene Linearformen. Zbl 0171.01003 Gruber, P.	5	1967
On the product of inhomogeneous linear forms. (Über das Produkt inhomogener Linearformen.) Zbl 0153.07102 Gruber, Peter	1	1967

all cited Publications top 5 cited Publications

all top 5

Cited by 1,470 Authors

36	Henk, Martin
34	Böröczky, Karoly jun.
33	Gruber, Peter Manfred
25	Xiong, Ge
22	Werner, Elisabeth M.
17	Ludwig, Monika
16	Hug, Daniel
16	Zong, Chuanming
15	Schymura, Matthias
14	Averkov, Gennadiy
14	Fukshansky, Lenny
13	Zamfirescu, Tudor I.
12	Aliev, Iskander M.
12	Hernández Cifre, María A.
12	Leng, Gangsong
11	Artstein-Avidan, Shiri
11	Cheng, Lixin
11	Fodor, Ferenc
11	Gardner, Richard J.
11	Reitzner, Matthias
11	Schütt, Carsten
10	Kim, Hark-Mahn
10	Rassias, John Michael
10	Ye, Deping
9	Bianchi, Gabriele
9	Gronchi, Paolo
9	Lángi, Zsolt
9	Martini, Horst
9	Schneider, Rolf G.
9	Vîlcu, Costin
9	Yepes Nicolás, Jesús
8	Lin, Youjiang
8	Lutwak, Erwin
8	Oertel, Timm
8	Raka, Madhu
8	Wills, Jörg M.
8	Zhou, Yu
8	Zhu, Sanguo
8	Zou, Du
7	Bétermin, Laurent
7	González Merino, Bernardo
7	Gritzmann, Peter
7	Jung, Soon-Mo
7	Milman, Vitali D.
7	Slomka, Boaz A.
7	Wang, Wei
7	Yang, Deane
7	Zhang, Gaoyong
6	Brzdęk, Janusz
6	De Loera, Jesús A.
6	Gómez, Eugenia Saorín
6	Jun, Kil-Woung
6	Li, Aijun
6	Meyer, Mathieu
6	Naszódi, Márton
6	Santos, Francisco
6	Sun, Longfa
6	Weismantel, Robert
6	Xue, Fei
6	Zhu, Baocheng
5	Betke, Ulrich
5	Freyer, Ansgar
5	Haberl, Christoph
5	Hans-Gill, Rajinder J.
5	Hoehner, Steven D.
5	Horváth, Ákos G.
5	Itoh, Jin-ichi
5	Kamenev, Georgy K.
5	Kathuria, Leetika
5	Linke, Eva
5	Liu, Lijuan
5	Molchanov, Ilya S.
5	Parapatits, Lukas
5	Ramharter, Gerhard
5	Reisner, Shlomo
5	Rotem, Liran
5	Rouyer, Joël
5	Schürmann, Achill
5	Šír, Zbyněk
5	Soltan, Valeriu
5	Tabachnikov, Serge L.
5	Ushakov, Vladimir Nikolaevich
5	Wu, Yuchi
5	Xi, Dongmeng
5	Xiong, Jiawei
4	Abardia-Evéquoz, Judit
4	Alfakih, Abdo Y.
4	Arya, Sunil
4	Babenko, Vladyslav Fedorovych
4	Badora, Roman
4	Balashov, Maxim Viktorovich
4	Besau, Florian
4	Bialy, Misha
4	Colesanti, Andrea
4	da Fonseca, Guilherme Dias
4	Dai, Duanxu
4	Dai, Jin
4	El-Fassi, Iz-Iddine
4	German, Oleg N.
4	Graf, Siegfried
...and 1,370 more Authors

all top 5

Cited in 337 Serials

65	Discrete & Computational Geometry
61	Advances in Mathematics
51	Journal of Mathematical Analysis and Applications
44	Monatshefte für Mathematik
32	Proceedings of the American Mathematical Society
27	Transactions of the American Mathematical Society
24	Advances in Applied Mathematics
21	The Journal of Geometric Analysis
20	Mathematika
19	Geometriae Dedicata
18	Journal of Functional Analysis
17	Discrete Mathematics
16	Journal of Approximation Theory
15	Israel Journal of Mathematics
15	Mathematische Annalen
14	Beiträge zur Algebra und Geometrie
14	Journal of Number Theory
13	Archiv der Mathematik
13	Results in Mathematics
13	Computational Geometry
13	Aequationes Mathematicae
12	Mathematical Notes
12	European Journal of Combinatorics
12	Linear Algebra and its Applications
12	Mathematical Programming. Series A. Series B
12	Advances in Geometry
11	Mathematische Zeitschrift
11	Science China. Mathematics
10	Calculus of Variations and Partial Differential Equations
10	Acta Mathematica Sinica. English Series
9	Discrete Applied Mathematics
9	Journal of Soviet Mathematics
9	Acta Mathematica Scientia. Series B. (English Edition)
8	Acta Mathematica Hungarica
7	Computational Mathematics and Mathematical Physics
7	Bulletin of the American Mathematical Society. New Series
7	Journal de Théorie des Nombres de Bordeaux
7	Journal of Convex Analysis
7	Journal of the European Mathematical Society (JEMS)
7	Communications in Contemporary Mathematics
6	Communications in Mathematical Physics
6	Indian Journal of Pure & Applied Mathematics
6	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
6	Journal of Combinatorial Theory. Series A
6	Journal of Geometry
6	Journal of the London Mathematical Society. Second Series
6	Theoretical Computer Science
6	Topology and its Applications
6	Computer Aided Geometric Design
6	Journal of the American Mathematical Society
6	SIAM Journal on Discrete Mathematics
6	Annals of Mathematics. Second Series
6	Communications in Mathematics
5	Advances in Applied Probability
5	Periodica Mathematica Hungarica
5	The Annals of Probability
5	Constructive Approximation
5	Journal of Theoretical Probability
5	Expositiones Mathematicae
5	The Electronic Journal of Combinatorics
5	Abstract and Applied Analysis
5	Journal of Inequalities and Applications
5	Mathematical Inequalities & Applications
5	Proceedings of the Steklov Institute of Mathematics
5	Journal of Function Spaces
4	Archive for Rational Mechanics and Analysis
4	Information Processing Letters
4	Duke Mathematical Journal
4	Journal of Computer and System Sciences
4	Journal of Optimization Theory and Applications
4	Mathematische Nachrichten
4	Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
4	Numerische Mathematik
4	Combinatorica
4	Journal of Complexity
4	Revista Matemática Iberoamericana
4	International Journal of Approximate Reasoning
4	Forum Mathematicum
4	International Journal of Mathematics
4	Geometric and Functional Analysis. GAFA
4	Proceedings of the Indian Academy of Sciences. Mathematical Sciences
4	SIAM Journal on Optimization
4	Journal of Mathematical Sciences (New York)
4	Comptes Rendus. Mathématique. Académie des Sciences, Paris
4	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
4	Moscow Journal of Combinatorics and Number Theory
4	SIAM Journal on Applied Algebra and Geometry
3	Journal of Mathematical Physics
3	Nonlinearity
3	Studia Mathematica
3	The Mathematical Intelligencer
3	Annali di Matematica Pura ed Applicata. Serie Quarta
3	Bulletin of the London Mathematical Society
3	Bulletin de la Société Mathématique de France
3	Canadian Journal of Mathematics
3	Computing
3	Econometrica
3	Inventiones Mathematicae
3	Journal of Pure and Applied Algebra
3	Manuscripta Mathematica
...and 237 more Serials

all top 5

Cited in 58 Fields

778	Convex and discrete geometry (52-XX)
247	Number theory (11-XX)
122	Functional analysis (46-XX)
92	Differential geometry (53-XX)
89	Probability theory and stochastic processes (60-XX)
80	Operations research, mathematical programming (90-XX)
77	Computer science (68-XX)
75	Numerical analysis (65-XX)
62	Difference and functional equations (39-XX)
59	Combinatorics (05-XX)
55	Approximations and expansions (41-XX)
54	Measure and integration (28-XX)
50	Real functions (26-XX)
41	Geometry (51-XX)
36	Dynamical systems and ergodic theory (37-XX)
36	Calculus of variations and optimal control; optimization (49-XX)
35	General topology (54-XX)
34	Algebraic geometry (14-XX)
33	Partial differential equations (35-XX)
33	Operator theory (47-XX)
31	Statistics (62-XX)
30	Information and communication theory, circuits (94-XX)
25	Linear and multilinear algebra; matrix theory (15-XX)
17	Global analysis, analysis on manifolds (58-XX)
15	Group theory and generalizations (20-XX)
15	Statistical mechanics, structure of matter (82-XX)
14	Harmonic analysis on Euclidean spaces (42-XX)
14	Manifolds and cell complexes (57-XX)
12	Systems theory; control (93-XX)
11	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
10	Ordinary differential equations (34-XX)
9	Topological groups, Lie groups (22-XX)
9	Functions of a complex variable (30-XX)
9	Potential theory (31-XX)
9	Mechanics of deformable solids (74-XX)
8	Order, lattices, ordered algebraic structures (06-XX)
8	Several complex variables and analytic spaces (32-XX)
7	General and overarching topics; collections (00-XX)
7	Commutative algebra (13-XX)
7	Quantum theory (81-XX)
5	Mathematical logic and foundations (03-XX)
5	Mechanics of particles and systems (70-XX)
4	History and biography (01-XX)
4	Abstract harmonic analysis (43-XX)
4	Algebraic topology (55-XX)
4	Fluid mechanics (76-XX)
4	Biology and other natural sciences (92-XX)
3	Optics, electromagnetic theory (78-XX)
2	Nonassociative rings and algebras (17-XX)
2	Integral transforms, operational calculus (44-XX)
2	Integral equations (45-XX)
1	General algebraic systems (08-XX)
1	Field theory and polynomials (12-XX)
1	Associative rings and algebras (16-XX)
1	Special functions (33-XX)
1	Sequences, series, summability (40-XX)
1	Relativity and gravitational theory (83-XX)
1	Geophysics (86-XX)

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Cited by 1,470 Authors

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