An analogue of minimal surface theory in $\operatorname {SL}(n,\mathbf C)/\operatorname {SU}(n)$
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- by M. Kokubu, M. Takahashi, M. Umehara and K. Yamada
- Trans. Amer. Math. Soc. 354 (2002), 1299-1325
- DOI: https://doi.org/10.1090/S0002-9947-01-02935-X
- Published electronically: November 19, 2001
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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.References
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Bibliographic 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
- MR Author ID: 237419
- 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
- MR Author ID: 243885
- Email: kotaro@math.kyushu-u.ac.jp
- Received by editor(s): March 8, 2001
- Published electronically: November 19, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 354 (2002), 1299-1325
- MSC (2000): Primary 53A10; Secondary 53A35, 53A07
- DOI: https://doi.org/10.1090/S0002-9947-01-02935-X
- MathSciNet review: 1873007