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arXiv · 2007.03166

Totally umbilic surfaces in hyperbolic 3-manifolds of finite volume

Colin Adams·William H. Meeks III·Alvaro K. Ramos
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Abstract

We construct for every connected surface $S$ of finite negative Euler characteristic and every $H \in [0,1)$, a hyperbolic 3-manifold $N(S,H)$ of finite volume and a proper, two-sided, totally umbilic embedding $f\colon S\to N(S,H)$ with mean curvature $H$. Conversely, we prove that a complete, totally umbilic surface with mean curvature $H \in [0,1)$ embedded in a hyperbolic 3-manifold of finite volume must be proper and have finite negative Euler characteristic.

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Colin Adams, William H. Meeks III, Alvaro K. Ramos. 2020-07-07. Totally umbilic surfaces in hyperbolic 3-manifolds of finite volume. https://arxiv.org/abs/2007.03166

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