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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 PDF
Trans. Amer. Math. Soc. 354 (2002), 1299-1325 Request permission

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
  • 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