Powers and logarithms of convex bodies

Vitali Milman; Liran Rotem

doi:10.1016/j.crma.2017.09.002

Powers and logarithms of convex bodies

Translated title of the contribution: Powers and logarithms of convex bodies

Vitali Milman, Liran Rotem

School of Mathematical Sciences

Tel Aviv University

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

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.

Translated title of the contribution	Powers and logarithms of convex bodies
Original language	English
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

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2017.09.002

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title = "Powers and logarithms of convex bodies",

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.",

author = "Vitali Milman and Liran Rotem",

note = "Publisher Copyright: {\textcopyright} 2017 Acad{\'e}mie des sciences",

year = "2017",

month = sep,

doi = "10.1016/j.crma.2017.09.002",

language = "الإنجليزيّة",

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T1 - Powers and logarithms of convex bodies

AU - Milman, Vitali

AU - Rotem, Liran

PY - 2017/9

Y1 - 2017/9

N2 - 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.

AB - 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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U2 - 10.1016/j.crma.2017.09.002

DO - 10.1016/j.crma.2017.09.002

M3 - مقالة

SN - 1631-073X

VL - 355

SP - 981

EP - 986

JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

IS - 9

ER -

Powers and logarithms of convex bodies

Abstract

All Science Journal Classification (ASJC) codes

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