Conformal currents and the entropy of negatively curved three-manifolds
Differential Geometry
2024-05-28 v1 Dynamical Systems
Geometric Topology
Abstract
In this paper, we describe the intersection between geodesic and conformal currents on closed hyperbolic three-manifolds. We use this to prove some sharp bounds which involve the Liouville entropy of a negatively curved metric, the minimal surface entropy, and the area ratio. Using these ideas we also give a new proof of the Mostow Rigidity Theorem in the three-dimensional case.
Keywords
Cite
@article{arxiv.2405.16302,
title = {Conformal currents and the entropy of negatively curved three-manifolds},
author = {Fernando C. Marques and André Neves},
journal= {arXiv preprint arXiv:2405.16302},
year = {2024}
}
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35 pages