On isotropicity with respect to a measure

Liran Rotem

doi:10.1007/978-3-319-09477-9_27

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 language	English
Pages (from-to)	413-422
Number of pages	10
Journal	Lecture Notes in Mathematics
Volume	2116
DOIs	https://doi.org/10.1007/978-3-319-09477-9_27
State	Published - 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/978-3-319-09477-9_27

Cite this

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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.",

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AB - 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.

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DO - 10.1007/978-3-319-09477-9_27

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VL - 2116

SP - 413

EP - 422

JO - Lecture Notes in Mathematics

JF - Lecture Notes in Mathematics

ER -

On isotropicity with respect to a measure

Abstract

All Science Journal Classification (ASJC) codes

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