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arXiv · 2405.07598

Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume

Tommaso Cremaschi·Viola Giovannini·Jean-Marc Schlenker
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Abstract

We provide conditions under which a Riemann surface $X$ is the asymptotic boundary of a convex co-compact hyperbolic manifold, homeomorphic to a handlebody, of negative renormalized volume. We prove that this is the case when there are on $X$ enough closed curves of short enough hyperbolic length.

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Tommaso Cremaschi, Viola Giovannini, Jean-Marc Schlenker. 2024-05-13. Filling Riemann surfaces by hyperbolic Schottky manifolds of negative volume. https://arxiv.org/abs/2405.07598

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