| Résume | Let S be a connected surface with finite negative Euler characteristic and let H be a real number with absolute value less than one. In this talk we show that S appears as a properly embedded, totally umbilic surface with mean curvature H in a hyperbolic 3-manifold of finite volume. Conversely, a complete, totally umbilic surface with mean curvature H, embedded in a hyperbolic 3-manifold of finite volume must be proper and have finite, negative Euler characteristic. Joint work with Colin Adams and William Meeks. |
