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：Kristály, Alexandru[1,2]; Zhao, Wei[3]

机构：[1] Department of Economics, Babe?-Bolyai University, Cluj-Napoca, 400591, Romania; [2] Institute of Applied Mathematics, óbuda University, Budapest, 1034, Hungary; [3] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2021

外文期刊名：arXiv

收录：EI(收录号：20210162115)

语种：英文

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, Bishop-Gromov, log-Sobolev and Lichnerowicz inequalities) on irreversible structures. Copyright ? 2021, The Authors. All rights reserved.