Invariant measures and lower Ricci curvature bounds
| Autor: | Jaime Santos-Rodríguez |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Lie group Metric Geometry (math.MG) Curvature Potential theory Combinatorics Mathematics - Metric Geometry Differential Geometry (math.DG) Homogeneous FOS: Mathematics Mathematics::Metric Geometry 53C23 53C21 Invariant (mathematics) Analysis Ricci curvature Mathematics |
| DOI: | 10.48550/arxiv.1810.11327 |
| Popis: | Given a metric measure space $(X,d,\mathfrak{m})$ that satisfies the Riemannian Curvature Dimension condition, $RCD^*(K,N),$ and a compact subgroup of isometries $G \leq Iso(X)$ we prove that there exists a $G-$invariant measure, $\mathfrak{m}_G,$ equivalent to $\mathfrak{m}$ such that $(X,d,\mathfrak{m}_G)$ is still a $RCD^*(K,N)$ space. We also obtain some applications to Lie group actions on $RCD^*(K,N)$ spaces. We look at homogeneous spaces, symmetric spaces and obtain dimensional gaps for closed subgroups of isometries. Comment: 26 pages |
| Databáze: | OpenAIRE |
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