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arXiv · 1701.05704

Some functional inequalities on non-reversible Finsler manifolds

Shin-ichi Ohta
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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 $\Gamma$-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.

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Shin-ichi Ohta. 2017-01-20. Some functional inequalities on non-reversible Finsler manifolds. https://arxiv.org/abs/1701.05704

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