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Convex bodies: the Brunn-Minkowski theory. 2nd expanded ed.(English)Zbl 1287.52001

Encyclopedia of Mathematics and its Applications 151. Cambridge: Cambridge University Press (ISBN 978-1-107-60101-7/hbk; 978-1-139-00385-8/ebook). xxii, 736 p. (2014).
Publisher’s description: This second edition has been considerably expanded to reflect the rapid developments of the past two decades. It includes new chapters on valuations on convex bodies, on extensions like the \(L_p\) Brunn-Minkowski theory, and on affine constructions and inequalities. There are also many supplements and updates to the original chapters, and a substantial expansion of chapter notes and references.
See the review of the first edition in [Zbl 0798.52001].

MSC:

52-02 Research exposition (monographs, survey articles) pertaining to convex and discrete geometry
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52A39 Mixed volumes and related topics in convex geometry
52A40 Inequalities and extremum problems involving convexity in convex geometry
52A22 Random convex sets and integral geometry (aspects of convex geometry)
33C55 Spherical harmonics

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