Powers and logarithms of convex bodies

Vitali Milman; Liran Rotem

doi:10.1016/j.crma.2017.09.002

Powers and logarithms of convex bodies

Vitali Milman
, Liran Rotem

School of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Do we have enough examples of convex bodies that we truly understand? Is out standard set of examples diverse enough to understand convexity? In this note, we will dramatically increase our set of examples. More specifically, we will present several new constructions of convex bodies: the geometric mean of two convex bodies, the power function K^α (which in general exists only for |α|≤1), and even the logarithm log⁡K.

Original language	English (US)
Pages (from-to)	981-986
Number of pages	6
Journal	Comptes Rendus Mathematique
Volume	355
Issue number	9
DOIs	https://doi.org/10.1016/j.crma.2017.09.002
State	Published - Sep 2017

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© 2017 Académie des sciences

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10.1016/j.crma.2017.09.002

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abstract = "Do we have enough examples of convex bodies that we truly understand? Is out standard set of examples diverse enough to understand convexity? In this note, we will dramatically increase our set of examples. More specifically, we will present several new constructions of convex bodies: the geometric mean of two convex bodies, the power function Kα (which in general exists only for |α|≤1), and even the logarithm log⁡K.",

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Powers and logarithms of convex bodies

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