Scalar curvature and volume entropy of hyperbolic 3-manifolds
Differential Geometry
2025-06-06 v3 Geometric Topology
Abstract
We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this construction gives counterexamples to a conjecture of I. Agol, P. Storm and W. Thurston.
Cite
@article{arxiv.2312.00138,
title = {Scalar curvature and volume entropy of hyperbolic 3-manifolds},
author = {Demetre Kazaras and Antoine Song and Kai Xu},
journal= {arXiv preprint arXiv:2312.00138},
year = {2025}
}
Comments
v3 update: some details are added. 15 pages, 2 figures. Final version, accepted by JEMS