Minimal Surface Entropy and Average Area Ratio
Differential Geometry
2025-06-23 v3 Dynamical Systems
Geometric Topology
Abstract
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. Our proofs use Ricci flow with surgery and laminar measures invariant under a PSL(2,R)-action.
Cite
@article{arxiv.2110.09451,
title = {Minimal Surface Entropy and Average Area Ratio},
author = {Ben Lowe and Andre Neves},
journal= {arXiv preprint arXiv:2110.09451},
year = {2025}
}
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