Year: 2025
Type: article
Abstract: : For every connected surface $S$ of finite negative Euler characteristic and every $H\in [0,1)$, we construct 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.
Source: American Journal of Mathematics
Authors: Colin Adams, William H. Meeks, Alvaro K. Ramos
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416618760