文献类型：期刊文献

英文题名：Absolutely continuous curves in Finsler-like spaces

作者：Zhang, Fue[1];Zhao, Wei[2]

机构：[1]Shihezi Univ, Dept Math, Shihezi 832000, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2024

卷号：96

外文期刊名：DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001244756200001)】；

语种：英文

外文关键词：Absolutely continuous curve; Finsler manifold; Wasserstein space; Gradient flow; Continuity equation

摘要：The present paper is devoted to the investigation of absolutely continuous curves in asymmetric metric spaces induced by Finsler structures. Firstly, for asymmetric spaces induced by Finsler manifolds, we show that three different kinds of absolutely continuous curves coincide when their domains are bounded closed intervals. As an application, a universal existence and regularity theorem for gradient flow is obtained in the Finsler setting. Secondly, we study absolutely continuous curves in Wasserstein spaces over Finsler manifolds and establish the Lisini structure theorem in this setting, which characterize the nature of absolutely continuous curves in Wasserstein spaces in terms of dynamical transference plans concentrated on absolutely continuous curves in base Finsler manifolds. Besides, a close relation between continuity equations and absolutely continuous curves in Wasserstein spaces is founded. Last but not least, we also consider nonsmooth "Finsler-like" spaces, in which case most of the aforementioned results remain valid. Various model examples are constructed in this paper, which point out genuine differences between the asymmetric and symmetric settings. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.