Tohoku Mathematical Journal

Minimal maps between the hyperbolic discs and generalized Gauss maps of maximal surfaces in the anti-de Sitter 3-space

Reiko Aiyama, Kazuo Akutagawa, and Tom Y. H. Wan

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Problems related to minimal maps are studied. In particular, we prove an existence result for the Dirichlet problem at infinity for minimal diffeomorphisms between the hyperbolic discs. We also give a representation formula for a minimal diffeomorphism between the hyperbolic discs by means of the generalized Gauss map of a complete maximal surface in the anti-de Sitter 3-space.

Article information

Tohoku Math. J. (2), Volume 52, Number 3 (2000), 415-429.

First available in Project Euclid: 3 May 2007

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Zentralblatt MATH identifier

Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53C50: Lorentz manifolds, manifolds with indefinite metrics


Aiyama, Reiko; Akutagawa, Kazuo; Wan, Tom Y. H. Minimal maps between the hyperbolic discs and generalized Gauss maps of maximal surfaces in the anti-de Sitter 3-space. Tohoku Math. J. (2) 52 (2000), no. 3, 415--429. doi:10.2748/tmj/1178207821.

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