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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An analogue of minimal surface theory in $\operatorname{SL}(n,\mathbf C)/\operatorname{SU}(n)$


Authors: M. Kokubu, M. Takahashi, M. Umehara and K. Yamada
Journal: Trans. Amer. Math. Soc. 354 (2002), 1299-1325
MSC (2000): Primary 53A10; Secondary 53A35, 53A07
Published electronically: November 19, 2001
MathSciNet review: 1873007
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Abstract: We shall discuss the class of surfaces with holomorphic right Gauss maps in non-compact duals of compact semi-simple Lie groups (e.g. $\operatorname{SL}(n,\mathbf{C})/\operatorname{SU}(n)$), which contains minimal surfaces in $\mathbf{R}^n$ and constant mean curvature $1$ surfaces in $\mathcal{H}^3$. A Weierstrass type representation formula and a Chern-Osserman type inequality for such surfaces are given.


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Additional Information

M. Kokubu
Affiliation: Department of Natural Science, School of Engineering, Tokyo Denki University, 2-2, Kanda-Nishiki-Cho, Chiyoda-Ku, Tokyo, 101-8457 Japan
Email: kokubu@cck.dendai.ac.jp

M. Takahashi
Affiliation: Department of General Education, Kurume National College of Technology, Kurume, Fukuoka 830-8555, Japan
Email: taka@GES.kurume-nct.ac.jp

M. Umehara
Affiliation: Department of Mathematics, Faculty of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan
Email: umehara@math.sci.hiroshima-u.ac.jp

K. Yamada
Affiliation: Faculty of Mathematics, Kyushu University 36, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan
Email: kotaro@math.kyushu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02935-X
PII: S 0002-9947(01)02935-X
Received by editor(s): March 8, 2001
Published electronically: November 19, 2001
Article copyright: © Copyright 2001 American Mathematical Society