The isotropy constant and boundary properties of convex bodies

Mathieu Meyer; Shlomo Reisner

doi:10.1090/proc/13143

The isotropy constant and boundary properties of convex bodies

Mathieu Meyer, Shlomo Reisner

Department of Mathematics

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

Abstract

Let Kⁿ be the set of all convex bodies in ℝⁿ endowed with the Hausdorff distance. We prove that if K ∈ Kⁿ has positive generalized Gauss curvature at some point of its boundary, then K is not a local maximizer for the isotropy constant L_K.

Original language	English
Pages (from-to)	3935-3947
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	144
Issue number	9
DOIs	https://doi.org/10.1090/proc/13143
State	Published - 2016

Bibliographical note

Publisher Copyright:
© 2016 American Mathematical Society.

Keywords

Convex bodies
Isotropy

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "The isotropy constant and boundary properties of convex bodies",

abstract = "Let Kn be the set of all convex bodies in ℝn endowed with the Hausdorff distance. We prove that if K ∈ Kn has positive generalized Gauss curvature at some point of its boundary, then K is not a local maximizer for the isotropy constant LK.",

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author = "Mathieu Meyer and Shlomo Reisner",

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doi = "10.1090/proc/13143",

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journal = "Proceedings of the American Mathematical Society",

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AB - Let Kn be the set of all convex bodies in ℝn endowed with the Hausdorff distance. We prove that if K ∈ Kn has positive generalized Gauss curvature at some point of its boundary, then K is not a local maximizer for the isotropy constant LK.

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KW - Isotropy

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DO - 10.1090/proc/13143

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JO - Proceedings of the American Mathematical Society

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The isotropy constant and boundary properties of convex bodies

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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