Spectral gap for some invariant log-concave probability measures

Abstract

We show that the conjecture of Kannan, Lovász, and Simonovits on isoperimetric properties of convex bodies and log-concave measures, is true for log-concave measures of the form $\rho (|x{|}_B)dx$ on ${\mathbb{R}}^n$ and $\rho (t,|x{|}_B)dx$ on ${\mathbb{R}}^{1+n}$, where $|x{|}_B$ is the norm associated to any convex body $B$ already satisfying the conjecture. In particular, the conjecture holds for convex bodies of revolution.

To appear in Mathematika. This version can differ from the one published in Mathematika

References in corpus (1)

• An isoperimetric inequality on the ${\ell }_p$ balls

Cited by in corpus (8)

• Local $L^p$-Brunn-Minkowski inequalities for $p<1$
• Order statistics and concentration of l_r norms for log-concave vectors
• Spectral gaps, symmetries and log-concave perturbations
• Spectral gap for spherically symmetric log-concave probability measures, and beyond
• Moments of unconditional logarithmically concave vectors
• The variance conjecture on hyperplane projections of l_p^n balls
• The variance conjecture on projections of the cube
• The KLS Isoperimetric Conjecture for Generalized Orlicz Balls