Affine images of isotropic measures

Károly J. Böröczky; Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.4310/jdg/1424880981

Affine images of isotropic measures

Károly J. Böröczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Mathematics

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

Abstract

Necessary and sufficient conditions are given in order for a Borel measure on the Euclidean sphere to have an affine image that is isotropic. A sharp reverse affine isoperimetric inequality for Borel measures on the sphere is presented. This leads to sharp reverse affine isoperimetric inequalities for convex bodies.

Original language	English (US)
Pages (from-to)	407-442
Number of pages	36
Journal	Journal of Differential Geometry
Volume	99
Issue number	3
DOIs	https://doi.org/10.4310/jdg/1424880981
State	Published - Mar 1 2015

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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title = "Affine images of isotropic measures",

abstract = "Necessary and sufficient conditions are given in order for a Borel measure on the Euclidean sphere to have an affine image that is isotropic. A sharp reverse affine isoperimetric inequality for Borel measures on the sphere is presented. This leads to sharp reverse affine isoperimetric inequalities for convex bodies.",

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AU - Böröczky, Károly J.

AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

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Y1 - 2015/3/1

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Affine images of isotropic measures

Abstract

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