Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes

Autor:	Braun, Mathias, Ohta, Shin-ichi
Rok vydání:	2023
Předmět:	Mathematics - Differential Geometry General Relativity and Quantum Cosmology Mathematics - Metric Geometry 53C50 53C60 58E10 83C99
Zdroj:	Trans. Amer. Math. Soc. 377 (2024), 3529-3576
Druh dokumentu:	Working Paper
Popis:	We prove that a Finsler spacetime endowed with a smooth reference measure whose induced weighted Ricci curvature $\smash{\mathrm{Ric}_N}$ is bounded from below by a real number $K$ in every timelike direction satisfies the timelike curvature-dimension condition $\smash{\mathrm{TCD}_q(K,N)}$ for all $q\in (0,1)$. A nonpositive-dimensional version ($N \le 0$) of this result is also shown. Our discussion is based on the solvability of the Monge problem with respect to the $q$-Lorentz-Wasserstein distance as well as the characterization of $q$-geodesics of probability measures. One consequence of our work is the sharp timelike Brunn-Minkowski inequality in the Lorentz-Finsler case. Comment: 56 pages. Comments welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.04389 Zobrazit plný text záznamu View this record from Arxiv