Flux for mean curvature 1 surfaces

in hyperbolic 3-space, and applications

Authors:
Wayne Rossman, Masaaki Umehara and Kotaro Yamada

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2147-2154

MSC (1991):
Primary 53A10; Secondary 53A35, 53A42

DOI:
https://doi.org/10.1090/S0002-9939-99-04892-3

Published electronically:
March 3, 1999

MathSciNet review:
1605941

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Abstract | References | Similar Articles | Additional Information

Abstract: Using the Bryant representation, we define a flux on homology classes of CMC- surfaces in , satisfying a balancing formula which is useful to show nonexistence of certain kinds of complete CMC- surfaces.

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Additional Information

**Wayne Rossman**

Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka 812-8581 Japan

Address at time of publication:
Department of Mathematics, Faculty of Science, Kobe University, Rokko, Kobe 657-8501, Japan

Email:
wayne@math.kyushu-u.ac.jp, wayne@math.kobe-u.ac.jp

**Masaaki Umehara**

Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043 Japan

Address at time of publication:
Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

Email:
umehara@math.wani.osaka-u.ac.jp, umehara@math.sci.hiroshima-u.ac.jp

**Kotaro Yamada**

Affiliation:
Department of Mathematics, Faculty of Science, Kumamoto University, Kumamoto 860-8555 Japan

Email:
kotaro@gpo.kumamoto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-99-04892-3

Received by editor(s):
October 15, 1997

Published electronically:
March 3, 1999

Additional Notes:
The authors were supported by Volkswagen-Stiftung (RiP Program in Mathematisches Forschungsinstitut Oberwolfach). The third author was supported by the Inamori Foundation.

Communicated by:
Peter Li

Article copyright:
© Copyright 1999
American Mathematical Society