On isotropicity with respect to a measure

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Abstract

A body C is said to be isotropic with respect to a measure µ if the function (Formula presented.) is constant on the unit sphere. In this note, we extend a result of Bobkov, and prove that every body can be put in isotropic position with respect to any rotation invariant measure. When the body C is convex, and the measure µ is log-concave, we relate the isotropic position with respect to µ to the famous M -position, and give bounds on the isotropic constant.

Original languageEnglish
Pages (from-to)413-422
Number of pages10
JournalLecture Notes in Mathematics
Volume2116
DOIs
StatePublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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