English

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