SPECTRAL GAP FOR SOME INVARIANT LOG‐CONCAVE PROBABILITY MEASURES

Abstract

We show that the conjecture of Kannan, Lov\\'{a}sz, and Simonovits on\nisoperimetric properties of convex bodies and log-concave measures, is true for\nlog-concave measures of the form $\\rho(|x|_B)dx$ on $\\mathbb{R}^n$ and\n$\\rho(t,|x|_B) dx$ on $\\mathbb{R}^{1+n}$, where $|x|_B$ is the norm associated\nto any convex body $B$ already satisfying the conjecture. In particular, the\nconjecture holds for convex bodies of revolution.\n