Joint IAS/PU Groups and Dynamics Seminar

Consider a closed surface M of genus greater than or equal to 2. For negatively curved metrics on M and their corresponding geodesic flow, we can study the topological entropy, the Liouville entropy, and the mean root curvature. In 2004, Manning showed that the topological entropy strictly decreases along the normalized Ricci flow if we start with a metric of variable negative curvature and asked whether monotonicity holds for the Liouville entropy. In this talk, we answer Manning's question and show that the Liouville entropy strictly increases along the flow. This talk is based on joint work with Butt, Humbert, and Mitsutani.