The geometry of finite topology Bryant surfaces quasi-embedded in a hyperbolic space

International audienceWe prove that a finite topology properly embedded Bryant surface in a complete hyperbolic 3-manifold has finite total curvature. This permits us to describe the geometry of the ends. We prove that the universal covering of these surfaces is an handlebody of H(3). when the ambient hyperbolic 3-manifold is hyperbolic "-space the theorems we prove were established By Collin-Hauswirth-Rosenber