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arXiv · 2203.16971

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

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 $\partial M$.

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Roman Prosanov. 2022-03-31. Dual metrics on the boundary of strictly polyhedral hyperbolic 3-manifolds. https://arxiv.org/abs/2203.16971

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