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A Weierstrass type representation for minimal surfaces in Sol

Author(s): Jun-ichi Inoguchi; Sungwook Lee
Journal: Proc. Amer. Math. Soc. 136 (2008), 2209-2216.
MSC (2000): Primary 53A10, 53C15, 53C30
Posted: February 7, 2008
MathSciNet review: 2383527
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Abstract | References | Similar articles | Additional information

Abstract: The normal Gauss map of a minimal surface in the model space $\mathrm{Sol}$ of solvegeometry is a harmonic map with respect to a certain singular Riemannian metric on the extended complex plane.

References:

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2.: U. Abresch and H. Rosenberg, Generalized Hopf differentials, Mat. Contemp. 28 (2005), 1-28. MR 2195187 (2006h:53004)
3.: R. Aiyama and K. Akutagawa, The Dirichlet problem at infinity for harmonic map equations arising from constant mean curvature surfaces in the hyperbolic 3-space, Calc. Var. Partial Differential Equations 14 (2002), no. 4, 399-428. MR 1911823 (2004d:58021)
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Additional Information:

Jun-ichi Inoguchi
Affiliation: Department of Mathematics Education, Utsunomiya University, Utsunomiya, 321-8505, Japan
Email: inoguchi@cc.utsunomiya-u.ac.jp

Sungwook Lee
Affiliation: Department of Mathematics, University of Southern Mississippi, Southern Hall, Box 5045, Hattiesburg, Mississippi 39406-5045
Email: sunglee@usm.edu

DOI: 10.1090/S0002-9939-08-09161-2
PII: S 0002-9939(08)09161-2
Keywords: Solvable Lie groups, minimal surfaces
Received by editor(s): September 26, 2006
Posted: February 7, 2008
Additional Notes: The first author was partially supported by Kakenhi 18540068
Dedicated: Dedicated to Professor Takeshi Sasaki on his 60th birthday
Communicated by: Chuu-Lian Terng
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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