Conformal currents and the entropy of negatively curved three-manifolds
Abstract
We describe the intersection between geodesic and conformal currents on closed hyperbolic threemanifolds.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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Geometry & Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 30
- Issue
- 7
- Pages
- 2565–2598
- Publication date
- 13 August 2026
- Language
- EN