芬斯勒时空上的最优传输和时间性下里奇曲率边界

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2024-02-26 DOI:10.1090/tran/9126

Mathias Braun, Shin-ichi Ohta

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引用次数: 0

摘要

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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Optimal transport and timelike lower Ricci curvature bounds on Finsler spacetimes

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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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.