ON THE EXISTENCE OF SUPERGAUSSIAN DIRECTIONS ON CONVEX BODIES Academic Article uri icon

abstract

  • We study the question of whether every centred convex body K of volume 1 in ℝ n has "supergaussian directions", which means θ ∈ S n-1 such that |[{x ∈ K: | 〈 x, θ 〉 |̀ t int: K |〈 x, θ 〉 | d x \biggr | ̀ -ct2 for all 1 ≤ t ≤ 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. © 2012 Copyright University College London.

author list (cited authors)

  • Paouris, G.

citation count

  • 9

publication date

  • July 2012

publisher