A Picard type theorem for Hyperbolic Gauss Map of CMC-1 Surfaces in Hyperbolic 3-space and de Sitter 3-space

Abstract

In a recent paper Jorge and Mercuri proved that the image of Gauss map of a complete non flat minimal surfaces in R3 with finite total curvature omits at most 2 points. In this work we follow their idea and prove 3a similar result for CMC-1 with finite total curvature in H and CMC-1 faces with finite type and regular ends in S31.