Affiliation:
1. Department of Mathematics , Osaka University , Toyonaka, Osaka , Japan
Abstract
Abstract
We investigate the relation between the concentration and the product of metric measure spaces. We have the natural question whether, for two concentrating sequences of metric measure spaces, the sequence of their product spaces also concentrates. A partial answer is mentioned in Gromov’s book [4]. We obtain a complete answer for this question.
Subject
Applied Mathematics,Geometry and Topology,Analysis
Reference17 articles.
1. [1] J. Borsík and J. Doboš, On a product of metric spaces, Math. Slovaca 31 (1981), no. 2, 193–205 (English, with Russian summary).
2. [2] J. Doboš and Z. Piotrowski, Some remarks on metric preserving functions, Real Anal. Exchange 19 (1993/94), no. 1, 317–320.
3. [3] K. Funano and T. Shioya, Concentration, Ricci curvature, and eigenvalues of Laplacian, Geom. Funct. Anal. 23 (2013), no. 3, 888–936.
4. [4] M. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Reprint of the 2001 English edition, Modern Birkhäuser Classics, Birkhäuser Boston, Inc., Boston, MA, 2007.
5. [5] D. Kazukawa, R. Ozawa, and N. Suzuki, Stabilities of rough curvature dimension condition, J. Math. Soc. Japan 72 (2020), no. 2, 541–567.
Cited by
6 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