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The isotropy constant and boundary properties of convex bodies


Authors: Mathieu Meyer and Shlomo Reisner
Journal: Proc. Amer. Math. Soc. 144 (2016), 3935-3947
MSC (2010): Primary 46B20, 52A20, 53A05
DOI: https://doi.org/10.1090/proc/13143
Published electronically: April 25, 2016
MathSciNet review: 3513550
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Abstract: Let $ \mathcal {K}^n$ be the set of all convex bodies in $ \mathbb{R}^n$ endowed with the Hausdorff distance. We prove that if $ K\in \mathcal {K}^n$ has positive generalized Gauss curvature at some point of its boundary, then $ K$ is not a local maximizer for the isotropy constant $ L_K$.


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Additional Information

Mathieu Meyer
Affiliation: Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées UMR 8050, UPEMLV, UPEC, CNRS F-77454, Marne-la-Vallée, France
Email: mathieu.meyer@u-pem.fr

Shlomo Reisner
Affiliation: Department of Mathematics, University of Haifa, Haifa, 31905, Israel
Email: reisner@math.haifa.ac.il

DOI: https://doi.org/10.1090/proc/13143
Keywords: Convex bodies, isotropy
Received by editor(s): November 12, 2015
Published electronically: April 25, 2016
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2016 American Mathematical Society