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Conformal currents and the entropy of negatively curved three-manifolds

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arxiv 2405.16302 v1 pith:NCSQG63E submitted 2024-05-25 math.DG math.DSmath.GT

Fernando C. Marques , André Neves This is my paper · ORCID
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keywords entropyconformalcurrentscurvednegativelythree-manifoldsareabounds
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Minimal surface entropy and applications of Ricci flow on finite-volume hyperbolic 3-manifolds

    math.DG 2025-08 conditional novelty 6.0 of 10

    For finite-volume hyperbolic 3-manifolds, the hyperbolic metric uniquely minimizes minimal surface entropy among sectional curvature at most -1 metrics and uniquely maximizes it among scalar curvature at least -6 metr...

  2. Foliated Plateau problems, geometric rigidity and equidistribution of closed $k$-surfaces

    math.DG 2025-02 unverdicted

    A survey of foliated Plateau problems showing that area-entropy and marked-area-spectrum rigidity for k-surfaces mirror classical geodesic-flow rigidity.

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