Affine images of isotropic measures

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)407-442
Number of pages36
JournalJournal of Differential Geometry
Volume99
Issue number3
StatePublished - Mar 1 2015

Fingerprint

Isoperimetric Inequality
Borel Measure
Reverse
Convex Body
Euclidean
Necessary Conditions
Sufficient Conditions

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

Cite this

Affine images of isotropic measures. / Böröczky, Károly J.; Lutwak, Erwin; Yang, Deane; Zhang, Gaoyong.

In: Journal of Differential Geometry, Vol. 99, No. 3, 01.03.2015, p. 407-442.

Research output: Contribution to journalArticle

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