Some functional inequalities on non-reversible Finsler manifolds
Abstract
We continue our study of geometric analysis on (possibly non-reversible) Finsler manifolds, based on the Bochner inequality established by the author and Sturm. Following the approach of the -calculus a la Bakry et al, we show the dimensional versions of the Poincare--Lichnerowicz inequality, the logarithmic Sobolev inequality, and the Sobolev inequality. In the reversible case, these inequalities were obtained by Cavalletti--Mondino in the framework of curvature-dimension condition by means of the localization method. We show that the same (sharp) estimates hold also for non-reversible metrics.
Keywords
Cite
@article{arxiv.1701.05704,
title = {Some functional inequalities on non-reversible Finsler manifolds},
author = {Shin-ichi Ohta},
journal= {arXiv preprint arXiv:1701.05704},
year = {2022}
}
Comments
22 pages (no change from v3); Corrigendum is available at http://www4.math.sci.osaka-u.ac.jp/~sohta/ ; See also my book "Comparison Finsler geometry" https://link.springer.com/book/10.1007/978-3-030-80650-7