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Mathematics > Metric Geometry

arXiv:2203.16971 (math)
[Submitted on 31 Mar 2022 (v1), last revised 15 Mar 2024 (this version, v4)]

Title:Dual metrics on the boundary of strictly polyhedral hyperbolic 3-manifolds

Authors:Roman Prosanov
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Abstract:Let $M$ be a compact oriented 3-manifold with non-empty boundary consisting of surfaces of genii $>1$ such that the interior of $M$ is hyperbolizable. We show that for each spherical cone-metric $d$ on $\partial M$ such that all cone-angles are greater than $2\pi$ and the lengths of all closed geodesics that are contractible in $M$ are greater than $2\pi$ there exists a unique strictly polyhedral hyperbolic metric on $M$ such that $d$ is the induced dual metric on $\partial M$.
Subjects: Metric Geometry (math.MG); Geometric Topology (math.GT)
MSC classes: 52B70, 52A55, 53C50, 53C24, 57M50
Cite as: arXiv:2203.16971 [math.MG]
  (or arXiv:2203.16971v4 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.2203.16971

Submission history

From: Roman Prosanov [view email]
[v1] Thu, 31 Mar 2022 11:43:08 UTC (36 KB)
[v2] Fri, 1 Apr 2022 11:58:53 UTC (36 KB)
[v3] Fri, 9 Sep 2022 17:34:01 UTC (40 KB)
[v4] Fri, 15 Mar 2024 19:19:12 UTC (54 KB)
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