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arXiv · 2405.16302

Conformal currents and the entropy of negatively curved three-manifolds

Fernando C. Marques·André Neves
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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.

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Fernando C. Marques, André Neves. 2024-05-25. Conformal currents and the entropy of negatively curved three-manifolds. https://doi.org/10.2140/gt.2026.30.2565

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