Mean curvature 1 surfaces of Costa type in hyperbolic 3-space
by
Celso Jose da Costa
Universidade Federal Fluminense, Brazil

Oral Communication

In our talk we will show that for every member of the family of Costa-Hoffman-Meeks embedded minimal surfaces we can construct the cousin equivalent in the hyperbolic three space. The method of construction is based in works of Rossman, Umehara and Yamada. References:

[1] C. Costa. Example of a complete immersion in R3 of genus one and three embedded ends. Bol. Soc. Bras. Mat. Vol. 15 , 1 (47-54)

[2] D.Hoffman and W. Meeks. Embedded minimal surfaces of finite topology, Annals of Mathematics, 131, 1-34, (1990)

[3] W. Rossman, M. Umehara and K.Yamada. Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus. Tohoku Math. J., 49 (1997), 449-484.

Date received: July 27, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafh-43.