MEAN CURVATURE 1 SURFACES IN HYPERBOLIC 3-SPACE WITH LOW TOTAL CURVATURE II

Abstract

In this work, complete constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space with total absolute curvature at most 4$\pi$ are classified. This classification suggests that the Cohn-Vossen inequality can be sharpened for surfaces with odd numbers of ends, and a proof of this is given.