A Bakry-Émery Approach to Lipschitz Transportation on Manifolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-11 DOI:10.1007/s11118-024-10138-4

Pablo López-Rivera

引用次数: 0

Abstract

On weighted Riemannian manifolds we prove the existence of globally Lipschitz transport maps between the weight (probability) measure and log-Lipschitz perturbations of it, via Kim and Milman’s diffusion transport map, assuming that the curvature-dimension condition \(\varvec{\textrm{CD}(\rho _{1}, \infty )}\) holds, as well as a second order version of it, namely \(\varvec{\Gamma _{3} \ge \rho _{2} \Gamma _{2}}\). We get new results as corollaries to this result, as the preservation of Poincaré’s inequality for the exponential measure on \(\varvec{(0,+\infty )}\) when perturbed by a log-Lipschitz potential and a new growth estimate for the Monge map pushing forward the gamma distribution on \(\varvec{(0,+\infty )}\) (then getting as a particular case the exponential one), via Laguerre’s generator.

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积分榜上的 Lipschitz Transportation 的 Bakry-Émery 方法

在加权黎曼流形上，我们通过 Kim 和 Milman 的扩散传输映射证明了权重（概率）度量和它的对数-利普希兹扰动之间存在全局利普希兹传输映射、假设曲率维度条件 \(\varvec{\textrm{CD}(\rho _{1}, \infty )}\) 成立，以及它的二阶版本，即 \(\varvec{\Gamma _{3} \ge \rho _{2} \Gamma _{2}}\) 成立。作为这一结果的推论，我们得到了新的结果，如当受到对数-利普斯奇兹势能的扰动时，\(\varvec{(0,+\infty )}\) 上指数量的波恩卡莱不等式的保留，以及通过拉盖尔生成器，在\(\varvec{(0,+\infty )}\) 上推前伽马分布的蒙日映射的新的增长估计（然后作为一种特殊情况得到指数分布）。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.