Maximal Volume Entropy Rigidity for $RCD^*(-(N-1),N)$ (Joint work with Connell, Dai, Nunez-Zimbron, Suarez-Serrato, Wei)
Time and place
12:30 PM on Thursday, October 11th, 2018; NAC 6/114
Raquel Perales (Instituto de Matemáticas, UNAM)
Abstract
For $n$-dimensional Riemannian manifolds $M$ with Ricci curvature bounded below by $-(n-1)$, the volume entropy is bounded above by $n-1$. If $M$ is compact, it is known that the equality holds if and only if $M$ is hyperbolic. We show the same maximal entropy rigidity result holds for a class of metric measure spaces known as $RCD^*(K,N$ spaces. While the upper bound follows quickly, the rigidity case is quite involved due to the lack of a smooth structure on these spaces.
