Abstract
In this work, complete constant mean curvature $1$ (\cmcone{}) 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.
Citation
Wayne Rossman. Masaaki Umehara. Kotaro Yamada. "Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature. II." Tohoku Math. J. (2) 55 (3) 375 - 395, 2003. https://doi.org/10.2748/tmj/1113247480
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