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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Abstract

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

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

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178207821

Digital Object Identifier
doi:10.2748/tmj/1178207821

Mathematical Reviews number (MathSciNet)
MR2002e:58025

Zentralblatt MATH identifier
0978.53106

Subjects
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

Citation

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. https://projecteuclid.org/euclid.tmj/1178207821


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