Characterization of Low Dimensional RCD*(K, N) Spaces
| Autor: | Sajjad Lakzian, Yu Kitabeppu |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
metric measure spaces
Class (set theory) Characterization (mathematics) Low dimensional 01 natural sciences Measure (mathematics) Combinatorics Mathematics - Metric Geometry 53C21 51Fxx 0103 physical sciences Bishop-Gromov FOS: Mathematics Mathematics::Metric Geometry Limit (mathematics) 0101 mathematics Ricci curvature Riemannian Ricci curvature bound Mathematics QA299.6-433 Applied Mathematics 010102 general mathematics Metric Geometry (math.MG) Ahlfors regular curvaturedimension Hausdorff dimension Metric (mathematics) Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology Isoperimetric inequality Ricci limit spaces Analysis |
| Zdroj: | Analysis and Geometry in Metric Spaces, Vol 4, Iss 1 (2016) |
| ISSN: | 2299-3274 |
| DOI: | 10.1515/agms-2016-0007 |
| Popis: | In this paper, we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called $RCD^*(K,N)$ spaces) with \emph{non-empty} one dimensional regular sets. In particular, we prove that the class of Ricci limit spaces with $Ric \ge K$ and Hausdorff dimension $N$ and the class of $RCD^*(K,N)$ spaces coincide for $N < 2$ (They can be either complete intervals or circles). We will also prove a Bishop-Gromov type inequality ( that is ,roughly speaking, a converse to the L\'{e}vy-Gromov's isoperimetric inequality and was previously only known for Ricci limit spaces) which might be also of independent interest. Comment: version 3: 37 pp, to appear in AGMS |
| Databáze: | OpenAIRE |
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