Geometric Analysis and Topology Seminar

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Scalar Curvature, Minimal Surfaces, and Hyperbolizable Riemannian Manifolds

Speaker: Ben Lowe, Princeton University

Location: Online

Videoconference link: https://nyu.zoom.us/j/94747124588

Date: Wednesday, February 9, 2022, 11 a.m.

Synopsis:

On any closed hyperbolizable 3-manifold, we find a sharp relation between the minimal surface entropy (introduced by Calegari-Marques-Neves) and the average area ratio (introduced by Gromov), and we show that, among metrics g with scalar curvature greater than or equal to -6, the former is maximized by the hyperbolic metric. One corollary is to solve a conjecture of Gromov regarding the average area ratio. We also prove a sharp lower bound for the area in g of a surface homotopic to a totally geodesic surface in the hyperbolic metric. Our proofs use Ricci flow with surgery and laminar measures invariant under a PSL(2,R)-action. Most of the talk will be based on the paper (joint with Andre Neves) https://arxiv.org/abs/2110.09451.