Affiliation:
1. University of Bonn, Bonn , Germany
2. University of Warwick, Coventry , United Kingdom
Abstract
Abstract
The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure) spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N) metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.
Subject
Applied Mathematics,Geometry and Topology,Analysis
Reference32 articles.
1. [1] L. Ambrosio, N. Gigli, A. Mondino, and T. Rajala, Riemannian Ricci curvature lower bounds in metric measure spaces with infinite measure, Trans. Amer. Math. Soc., 367 (2015), pp. 4661-4701.
2. [2] L. Ambrosio, N. Gigli, and G. Savaré, Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below, Invent. Math., 195 (2014), pp. 289-391.
3. [3] , Metric measure spaces with Riemannian Ricci curvature bounded from below, Duke Math. J., 163 (2014), pp. 1405-1490.
4. [4] L. Ambrosio and S. Honda, New stability results for sequences of metric measure spaces with uniform Ricci bounds from below. Preprint, arXiv:1605.07908, (2016).
5. [5] L. Ambrosio, A. Mondino, and G. Savaré, Nonlinear diffusion equations and curvature conditions in metric measure spaces, preprint arXiv:1509.07273, to appear in Mem. Amer. Math. Soc.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Singular Weyl’s law with Ricci curvature bounded below;Transactions of the American Mathematical Society, Series B;2023-08-29
2. A Solution to Two Old Problems by Menger Concerning Angle Spaces;Mediterranean Journal of Mathematics;2022-08