## Tohoku Mathematical Journal 2003 September SECOND SERIES VOL. 55, NO. 3

 Tohoku Math. J. 55 (2003), 375-395

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

Dedicated to Professor Katsuei Kenmotsu on his sixtieth birthday

Author Wayne Rossman, Masaaki Umehara and Kotaro Yamada

(Received August 3, 2001)
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.

2000 Mathematics Subject Classification. Primary 53A10; Secondary 53A35, 53C42.