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Title:
Entropy Rigidities for RCD Space
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Abstract:
Volume entropy is a fundamental geometric invariant defined as the exponential growth rate of volumes of balls in the universal cover. It is a very subtle invariant which has been extensive studied in geometry, topology and dynamical systems. RCD spaces are the most general metric spaces which one can still talk about Ricci curvature lower bounds (and still in the Riemannian category). They contain the Ricci limit spaces and has attracted intensive attentions recently. We will report some of our recent joint work with Chris Connell, Jesus Nunez-Zimbron, Requel Perales, Pablo Suarez-Serrato and Guofang Wei about the generalization to RCD spaces of the volume entropy rigidity results, including the famous rigidity result of Besson-Courtois-Gallot.
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