Ideal polyhedral surfaces in Fuchsian manifolds

Roman Prosanov

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arXiv · 1804.05893

Ideal polyhedral surfaces in Fuchsian manifolds

Roman Prosanov

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Abstract

Let $S_{g,n}$ be a surface of genus $g > 1$ with $n>0$ punctures equipped with a complete hyperbolic cusp metric. Then it can be uniquely realized as the boundary metric of an ideal Fuchsian polyhedron. In the present paper we give a new variational proof of this result. We also give an alternative proof of the existence and uniqueness of a hyperbolic polyhedral metric with prescribed curvature in a given conformal class.

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Roman Prosanov. 2018-04-16. Ideal polyhedral surfaces in Fuchsian manifolds. https://arxiv.org/abs/1804.05893

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