English

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

R2 v1 2026-06-22T01:24:46.474Z