Maximal volume entropy rigidity for ${\mathsf{RCD}}^{\ast }(-(N-1),N)$ spaces

Chris Connell, Xianzhe Dai, Jesús Núñez-Zimbrón +3

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 e…