An analogue of minimal surface theory in
Authors:
M. Kokubu, M. Takahashi, M. Umehara and K. Yamada
Journal:
Trans. Amer. Math. Soc. 354 (2002), 12991325
MSC (2000):
Primary 53A10; Secondary 53A35, 53A07
Published electronically:
November 19, 2001
MathSciNet review:
1873007
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
Abstract: We shall discuss the class of surfaces with holomorphic right Gauss maps in noncompact duals of compact semisimple Lie groups (e.g. ), which contains minimal surfaces in and constant mean curvature surfaces in . A Weierstrass type representation formula and a ChernOsserman type inequality for such surfaces are given.
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 [CL]
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 [CO]
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 [F]
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 [H]
 S. Helgason, Differential Geometry, Lie groups, and Symmetric Spaces, Academic Press, New YorkSan FranciscoLondon, 1978. MR 80k:53081
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 M. Kokubu, M. Umehara and K. Yamada, Minimal surfaces that attain equality in the ChernOsserman inequality, preprint, math.DG/0102037.
 [L]
 H. B. Lawson, Lectures on minimal submanifolds (Volume 1), Publish or Perish Inc., 1980. MR 82d:53035b
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 W. Rossman, M. Umehara and K. Yamada, Irreducible constant mean curvature 1 surfaces in hyperbolic space with positive genus, Tôhoku Math. J. 49 (1997), 449484 MR 99a:53025
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Additional Information
M. Kokubu
Affiliation:
Department of Natural Science, School of Engineering, Tokyo Denki University, 22, KandaNishikiCho, ChiyodaKu, Tokyo, 1018457 Japan
Email:
kokubu@cck.dendai.ac.jp
M. Takahashi
Affiliation:
Department of General Education, Kurume National College of Technology, Kurume, Fukuoka 8308555, Japan
Email:
taka@GES.kurumenct.ac.jp
M. Umehara
Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, HigashiHiroshima 7398526, Japan
Email:
umehara@math.sci.hiroshimau.ac.jp
K. Yamada
Affiliation:
Faculty of Mathematics, Kyushu University 36, Hakozaki 6101, Higashiku, Fukuoka 8128581, Japan
Email:
kotaro@math.kyushuu.ac.jp
DOI:
http://dx.doi.org/10.1090/S000299470102935X
PII:
S 00029947(01)02935X
Received by editor(s):
March 8, 2001
Published electronically:
November 19, 2001
Article copyright:
© Copyright 2001
American Mathematical Society
