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ON THE EXISTENCE OF SUPERGAUSSIAN DIRECTIONS ON CONVEX BODIES

  • Grigoris Paouris (a1)

Abstract

We study the question of whether every centred convex body K of volume 1 in ℝn has “supergaussian directions”, which means θSn−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.

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ON THE EXISTENCE OF SUPERGAUSSIAN DIRECTIONS ON CONVEX BODIES

  • Grigoris Paouris (a1)

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