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Flux for mean curvature 1 surfaces in hyperbolic 3-space, and applications

Author(s): Wayne Rossman; Masaaki Umehara; Kotaro Yamada
Journal: Proc. Amer. Math. Soc. 127 (1999), 2147-2154.
MSC (1991): Primary 53A10; Secondary 53A35, 53A42
Posted: March 3, 1999
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Abstract: Using the Bryant representation, we define a flux on homology classes of CMC-$1$ surfaces in $\mathcal{H}^3$, satisfying a balancing formula which is useful to show nonexistence of certain kinds of complete CMC-$1$ 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: 10.1090/S0002-9939-99-04892-3
PII: S 0002-9939(99)04892-3
Received by editor(s): October 15, 1997
Posted: 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
Copyright of article: Copyright 1999, American Mathematical Society

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