%0 Journal Article
%T Logarithmically-concave moment measures I
%A B. Klartag
%J Mathematics
%D 2013
%I arXiv
%X We discuss a certain Riemannian metric, related to the toric Kahler-Einstein equation, that is associated in a linearly-invariant manner with a given log-concave measure in R^n. We use this metric in order to bound the second derivatives of the solution to the toric Kahler-Einstein equation, and in order to obtain spectral-gap estimates similar to those of Payne and Weinberger.
%U http://arxiv.org/abs/1309.2767v1