Analysis and Geometric Analysis Seminar
Ruojing JiangUniversity of Chicago
Average area ratio and minimal surface entropy of hyperbolic manifolds
Monday, February 6, 2023 - 2:40pm
On closed hyperbolic manifolds of dimension at least 3, I will introduce the definition of the average area ratio of a metric h with scalar curvature bounded below by -n(n-1) relative to the hyperbolic metric h_0. We will see that it attains the local minimum of one at h_0, which solves a local version of Gromov’s conjecture.
Additionally, I will survey the results of the minimal surface entropy for odd-dimensional hyperbolic manifolds, and discuss its relation to the average area ratio.