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ON THE EXISTENCE OF SUPERGAUSSIAN DIRECTIONS ON CONVEX BODIES

Part of: General convexity

Published online by Cambridge University Press:  24 November 2011

Grigoris Paouris
Grigoris Paouris*
Affiliation:
Department of Mathematics, Texas A & M University, College Station, TX 77843, U.S.A. (email: grigoris@math.tamu.edu)
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Abstract

We study the question of whether every centred convex body K of volume 1 in ℝn has “supergaussian directions”, which means θ∈Sn−1 such that for all , where c>0 is an absolute constant. We verify that a “random” direction is indeed supergaussian for isotropic convex bodies that satisfy the hyperplane conjecture. On the other hand, we show that if, for all isotropic convex bodies, a random direction is supergaussian then the hyperplane conjecture follows.

MSC classification

Secondary: 52A23: Asymptotic theory of convex bodies
Type
Research Article
Information
Mathematika , Volume 58 , Issue 2 , July 2012 , pp. 389 - 408
Copyright
Copyright © University College London 2012

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