Movatterモバイル変換


[0]ホーム

URL:


×

zbMATH Open — the first resource for mathematics

from until
Reset all

Examples

GeometrySearch for the termGeometry inany field. Queries arecase-independent.
Funct*Wildcard queries are specified by* (e .g.functions,functorial, etc.). Otherwise the search isexact.''Topological group'':Phrases (multi - words) should be set in''straight quotation marks''.
au: Bourbaki & ti: AlgebraSearch forauthorBourbaki andtitleAlgebra. Theand-operator & is default and can be omitted.
Chebyshev | TschebyscheffTheor-operator| allows to search forChebyshev orTschebyscheff.
Quasi* map* py: 1989The resulting documents havepublicationyear1989.
so:Eur* J* Mat* Soc* cc:14Search for publications in a particularsource with aMathematics SubjectClassificationcode in14.
cc:*35 ! any:ellipticSearch for documents about PDEs (prefix with * to search only primary MSC); the not-operator ! eliminates all results containing the wordelliptic.
dt: b & au: HilbertThedocumenttype is set tobooks; alternatively:j forjournal articles,a forbookarticles.
py: 2000 - 2015 cc:(94A | 11T)Numberranges when searching forpublicationyear are accepted . Terms can be grouped within( parentheses).
la: chineseFind documents in a givenlanguage .ISO 639 - 1 (opens in new tab) language codes can also be used.
st: c r sFind documents that arecited, havereferences and are from asingle author.

Fields

ab Text from the summary or review (for phrases use “. ..”)
an zbMATH ID, i.e.: preliminary ID, Zbl number, JFM number, ERAM number
any Includes ab, au, cc, en, rv, so, ti, ut
arxiv arXiv preprint number
au Name(s) of the contributor(s)
br Name of a person with biographic references (to find documents about the life or work)
cc Code from the Mathematics Subject Classification (prefix with* to search only primary MSC)
ci zbMATH ID of a document cited in summary or review
db Database: documents in Zentralblatt für Mathematik/zbMATH Open (db:Zbl), Jahrbuch über die Fortschritte der Mathematik (db:JFM), Crelle's Journal (db:eram), arXiv (db:arxiv)
dt Type of the document: journal article (dt:j), collection article (dt:a), book (dt:b)
doi Digital Object Identifier (DOI)
ed Name of the editor of a book or special issue
en External document ID: DOI, arXiv ID, ISBN, and others
in zbMATH ID of the corresponding issue
la Language (use name, e.g.,la:French, orISO 639-1, e.g.,la:FR)
li External link (URL)
na Number of authors of the document in question. Interval search with “-”
pt Reviewing state: Reviewed (pt:r), Title Only (pt:t), Pending (pt:p), Scanned Review (pt:s)
pu Name of the publisher
py Year of publication. Interval search with “-”
rft Text from the references of a document (for phrases use “...”)
rn Reviewer ID
rv Name or ID of the reviewer
se Serial ID
si swMATH ID of software referred to in a document
so Bibliographical source, e.g., serial title, volume/issue number, page range, year of publication, ISBN, etc.
st State: is cited (st:c), has references (st:r), has single author (st:s)
sw Name of software referred to in a document
ti Title of the document
ut Keywords

Operators

a & bLogical and (default)
a | bLogical or
!abLogical not
abc*Right wildcard
ab cPhrase
(ab c)Term grouping

See also ourGeneral Help.

Comparison of Monge-Ampère capacities.(English)Zbl 1470.32117

Summary: Let \((X,\omega)\) be a compact Kähler manifold. We prove that all Monge-Ampère capacities are comparable. Using this we give a direct proof of the integration by parts formula for non-pluripolar products recently proved by M. Xia.

MSC:

32W20 Complex Monge-Ampère operators
32U05 Plurisubharmonic functions and generalizations
32Q15 Kähler manifolds

Cite

References:

[1]E. Bedford and B. A. Taylor,The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), 1-44. ·Zbl 0315.31007
[2]E. Bedford and B. A. Taylor,A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40. ·Zbl 0547.32012
[3]R. J. Berman, S. Boucksom, V. Guedj and A. Zeriahi,A variational approach to complex Monge-Ampère equations, Publ. Math. Inst. Hautes Études Sci. 117 (2013), 179-245. ·Zbl 1277.32049
[4]Z. Błocki and S. Kołodziej,On regularization of plurisubharmonic functions on manifolds, Proc. Amer. Math. Soc. 135 (2007), 2089-2093. ·Zbl 1116.32024
[5]S. Boucksom, P. Eyssidieux, V. Guedj and A. Zeriahi,Monge-Ampère equations in big cohomology classes, Acta Math. 205 (2010), 199-262. ·Zbl 1213.32025
[6]I. Chiose,On the invariance of the total Monge-Ampère volume of Hermitian metrics, arXiv:1609.05945 (2016). ·Zbl 1348.32007
[7]D. Coman, V. Guedj and A. Zeriahi,Domains of definition of Monge-Ampère operators on compact Kähler manifolds, Math. Z. 259 (2008), 393-418. ·Zbl 1137.32015
[8]T. Darvas, E. Di Nezza and C. H. Lu,L1metric geometry of big cohomology classes, Ann. Inst. Fourier (Grenoble) 68 (2018), 3053-3086. ·Zbl 1505.53081
[9]T. Darvas, E. Di Nezza and C. H. Lu,Monotonicity of nonpluripolar products and complex Monge-Ampère equations with prescribed singularity, Anal. PDE 11 (2018), 2049-2087. ·Zbl 1396.32011
[10]T. Darvas, E. Di Nezza and C. H. Lu,On the singularity type of full mass currents in big cohomology classes, Compos. Math. 154 (2018), 380-409. ·Zbl 1398.32042
[11]T. Darvas, E. Di Nezza and C. H. Lu,Log-concavity of volume and complex Monge- Ampère equations with prescribed singularity, Math. Ann. 379 (2021), 95-132. ·Zbl 1460.32087
[12]T. Darvas, E. Di Nezza and C. H. Lu,The metric geometry of singularity types, J. Reine Angew. Math. 771 (2021), 137-170. ·Zbl 1503.32029
[13]T. Darvas and C. H. Lu,Geodesic stability, the space of rays and uniform convexity in Mabuchi geometry, Geom. Topol. 24 (2020), 1907-1967. ·Zbl 1479.32011
[14]J.-P. Demailly,Regularization of closed positive currents of type(1,1)by the flow of a Chern connection, in: Contributions to Complex Analysis and Analytic Geometry, Aspects Math. E26, Vieweg, Braunschweig, 1994, 105-126. ·Zbl 0824.53064
[15]E. Di Nezza and C. H. Lu,Generalized Monge-Ampère capacities, Int. Math. Res. Notices 2015, 7287-7322. ·Zbl 1330.32013
[16]E. Di Nezza and C. H. Lu,Complex Monge-Ampère equations on quasi-projective varieties, J. Reine Angew. Math. 727 (2017), 145-167. ·Zbl 1380.32024
[17]E. Di Nezza and S. Trapani,Monge-Ampère measures on contact sets, Math. Res. Lett., to appear; arXiv:1912.12720 (2019).
[18]V. Guedj, C. H. Lu and A. Zeriahi,Plurisubharmonic envelopes and supersolutions, J. Differential Geom. 113 (2019), 273-313. ·Zbl 1435.32041
[19]V. Guedj and A. Zeriahi,Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal. 15 (2005), 607-639. ·Zbl 1087.32020
[20]V. Guedj and A. Zeriahi,The weighted Monge-Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal. 250 (2007), 442-482. ·Zbl 1143.32022
[21]V. Guedj and A. Zeriahi,Degenerate Complex Monge-Ampère Equations, EMS Tracts Math. 26, Eur. Math. Soc., Zürich, 2017. ·Zbl 1373.32001
[22]S. Kołodziej,The complex Monge-Ampère equation, Acta Math. 180 (1998), 69-117. ·Zbl 0913.35043
[23]C. H. Lu and V. D. Nguyên,Complex Hessian equations with prescribed singularity on compact Kähler manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci., to appear; arXiv:1909.02469 (2019).
[24]J. Ross and D. Witt Nyström,Analytic test configurations and geodesic rays, J. Symplectic Geom. 12 (2014), 125-169. ·Zbl 1300.32021
[25]D.-V. Vu,Generalized non-pluripolar products of currents, arXiv:2004.11111 (2020).
[26]D. Witt Nyström,Monotonicity of non-pluripolar Monge-Ampère masses, Indiana Univ. Math. J. 68 (2019), 579-591. ·Zbl 1422.32041
[27]M. Xia,Integration by parts formula for non-pluripolar product, arXiv:1907.06359 (2019).
[28]S.-T. Yau,On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation. I, Comm. Pure Appl. Math. 31 (1978) ·Zbl 0362.53049
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
© 2025FIZ Karlsruhe GmbHPrivacy PolicyLegal NoticesTerms & Conditions
  • Mastodon logo
 (opens in new tab)

[8]ページ先頭

©2009-2025 Movatter.jp