February 07, 2020
4:00 PM - 6:00 PM
Math Tower P-131
|Alena Erchenko, Stony Brook University|
Rigidity of topological entropy on manifolds carrying a metric of constant negative curvature
Let X be a compact connected locally symmetric Riemannian manifold of negative curvature. For any Riemannian manifold Y topologically related to X, Besson, Courtois, and Gallot proved a relation between the volume entropies of Y and X. In particular, their result implies Mostow's rigidity theorem. We will discuss the steps in the proof of their result in the case when X has constant negative curvature, Y is negatively curved, and X and Y are homotopy equivalent. The main reference is "Minimal entropy and Mostow's rigidity theorems" by Besson, Courtois, and Gallot.