Logarithmically-concave moment measures I
Analysis of PDEs
2013-09-12 v1 Differential Geometry
Metric Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1309.2767,
title = {Logarithmically-concave moment measures I},
author = {B. Klartag},
journal= {arXiv preprint arXiv:1309.2767},
year = {2013}
}
Comments
27 pages