Surfaces de Bryant dans [formula omitted] de type fini

Abstract

We define the notion of Bryant surfaces of finite type: an annular end of a Bryant surface is said to be of finite type if its hyperbolic Gauss map is of finite growth (in the sense of Nevanlinna), and a Bryant surface is said to be of finite type if it is of finite conformal type and if all its ends are of finite type. We prove that a Bryant surface of finite total curvature is of finite type.