Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-26 DOI:10.1090/tran/9126

Mathias Braun, Shin-ichi Ohta

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引用次数: 0

Abstract

We prove that a Finsler spacetime endowed with a smooth reference measure whose induced weighted Ricci curvature R i c N \mathrm {Ric}_N is bounded from below by a real number K K in every timelike direction satisfies the timelike curvature-dimension condition T C D q ( K , N ) \mathrm {TCD}_q(K,N) for all q ∈ ( 0 , 1 ) q\in (0,1) . The converse and a nonpositive-dimensional version ( N ≤ 0 N \le 0 ) of this result are also shown. Our discussion is based on the solvability of the Monge problem with respect to the q q -Lorentz–Wasserstein distance as well as the characterization of q q -geodesics of probability measures. One consequence of our work is the sharp timelike Brunn–Minkowski inequality in the Lorentz–Finsler case.

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芬斯勒时空上的最优传输和时间性下里奇曲率边界

我们证明了一个赋有光滑参考量度的芬斯勒时空，其诱导加权里奇曲率 R i c N \mathrm {Ric}_N 在每个时间方向上自下而上被实数 K K 限定，满足所有 q∈ ( 0 , 1 ) q\in (0,1) 的时间曲率维度条件 T C D q ( K , N ) \mathrm {TCD}_q(K,N) 。这个结果的反面和非正维版本 ( N ≤ 0 N \le 0 ) 也被展示出来。我们的讨论基于 Monge 问题关于 q q -Lorentz-Wasserstein 距离的可解性以及概率测度的 q q -geodesics 的特征。我们工作的一个结果是洛伦兹-芬斯勒情况下的尖锐时间状布伦-闵科夫斯基不等式。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.