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arXiv · 1810.11327

Invariant measures and lower Ricci curvature bounds

Jaime Santos-Rodríguez
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Abstract

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.

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Jaime Santos-Rodríguez. 2018-10-26. Invariant measures and lower Ricci curvature bounds. https://arxiv.org/abs/1810.11327

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