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

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