Proceedings of the American Mathematical Society

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
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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.

1.: U. Abresch and H. Rosenberg, The Hopf differential for constant mean curvature surfaces in $\mathbb{S}^{2}\times \mathbb{R}$ and $\mathbb{H}^{2}\times \mathbb{R}$ , Acta Math. 193 (2004), no. 2, 141-174. MR 2134864 (2006h:53003)
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)
4.: D. A. Berdinskiĭ and I. A. Taĭmanov, Surfaces in three-dimensional Lie groups (in Russian), Sibirsk. Mat. Zh. 46 (2005), no. 6, 1248-1264; translation in Siberian Math. J. 46 (2005), no. 6, 1005-1019. MR 2195027 (2006j:53087)
5.: J. Inoguchi, Minimal surfaces in -dimensional solvable Lie groups, Chinese Ann. Math. B. 24 (2003), 73-84. MR 1966599 (2004a:53006)
6.: J. Inoguchi, Minimal surfaces in -dimensional solvable Lie groups. II, Bull. Austral. Math. Soc. 73 (2006), 365-374. MR 2230647 (2007a:53008)
7.: J. Inoguchi, Minimal surfaces in the -dimensional Heisenberg group, to appear Differential Geometry-Dynamical Systems 10 (2008) (electronic).
8.: M. Kokubu, Weierstrass representation for minimal surfaces in hyperbolic space, Tôhoku Math. J. 49 (1997), 367-377. MR 1464184 (98f:53008)
9.: I. A. Taĭmanov, Two-dimensional Dirac operator and the theory of surfaces, Uspekhi Mat. Nauk 61 (2006), no. 1 (367), 85-164; translation in Russian Math. Surveys 61 (2006), no. 1, 79-159. MR 2239773 (2007k:37098)
10.: W. M. Thurston, Three-Dimensional Geometry and Topology. I, Princeton Math. Series., vol. 35 (S. Levy, ed.), 1997. MR 1435975 (97m:57016)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53A10, 53C15, 53C30

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.

Jun-ichi Inoguchi, Minimal surfaces in the 3-dimensional Heisenberg group, Differ. Geom. Dyn. Syst. 10 (2008), 163-169.

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