Mathematics Colloquium - Raquel Perales (Instituto de Matemáticas, UNAM)
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.
October 11, 2018
12:30 PM — 1:30 PM
The City College of New York
160 Convent Avenue & 138th Street
North Academic Center