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Scalar curvature and volume entropy of hyperbolic 3-manifolds

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arxiv 2312.00138 v3 pith:NNMZFK4A submitted 2023-11-30 math.DG math.GT

Demetre Kazaras , Antoine Song , Kai Xu This is my paper · ORCID
classification math.DGmath.GT
keywords curvatureentropyhyperbolicscalarvolumeadmitsagolclosed
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We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this construction gives counterexamples to a conjecture of I. Agol, P. Storm and W. Thurston.

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Cited by 1 Pith paper

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  1. Codimension 2 drawstrings with scalar curvature lower bounds

    math.DG 2025-01 conditional novelty 7.0 of 10

    Kazaras and Xu construct drawstring metrics along arbitrary codimension-2 submanifolds with scalar curvature almost bounded below, yielding new collapsed limits and a claimed but flawed Llarull counterexample.

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