Um teorema tipo-Picard para a aplicação de Gauss hiperbólica de superfícies CMC-1 imersas no espaço hiperbólico e no espaço de Sitter 3-dimensional.

Abstract

In this work we study the hyperbolic Gauss map of CMC-1 immersed surfaces in hyperbolic 3-space, also known as Bryant surfaces, and of CMC-1 faces in the de Sitter 3-space. We obtain a sharp estimate of the missing points of this map when the surface has finite total curvature, providing a Picard-type theorem for hyperbolic Gauss map in these spaces.