文献类型：期刊文献

英文题名：On the geometry of irreversible metric-measure spaces: Convergence, stability and analytic aspects

作者：Kristaly, Alexandru[1,2];Zhao, Wei[3]

机构：[1]Babes Bolyai Univ, Dept Econ, Cluj Napoca 400591, Romania;[2]Obuda Univ, Inst Appl Math, H-1034 Budapest, Hungary;[3]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2022

卷号：158

起止页码：216

外文期刊名：JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000744537600008)】；

基金：A. Kristaly was supported by the UEFISCDI/CNCS grant PN-III-P4-ID-PCE_2020-1001. W. Zhao was supported National Natural Science Foundation of China (No. 11761058) and Natural Science Foundation of Shanghai (No. 21ZR1418300, No. 19ZR1411700).

语种：英文

外文关键词：Irreversible metric space; Gromov-Hausdorff topology; Optimal transport; Weak curvature-dimension condition; Finsler manifold

摘要：The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by J. Lott, K.-T. Sturm and C. Villani, the noncompact case provides various surprising phenomena. Since the reversibility of noncompact irreversible spaces might be infinite, it is motivated to introduce a suitable nondecreasing function that bounds the reversibility of larger and larger balls. By this approach, we are able to prove satisfactory convergence/stability results in a suitable - reversibility depending - Gromov-Hausdorff topology. A wide class of irreversible spaces is provided by Finsler manifolds, which serve to construct various model examples by pointing out genuine differences between the reversible and irreversible settings. We conclude the paper by proving various geometric and functional inequalities (as Brunn-Minkowski, BishopGromov, log-Sobolev and Lichnerowicz inequalities) on irreversible structures. (c) 2021 Elsevier Masson SAS. All rights reserved.