Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 52, Number 3 (2000), 415-429.
Minimal maps between the hyperbolic discs and generalized Gauss maps of maximal surfaces in the anti-de Sitter 3-space
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.
Tohoku Math. J. (2), Volume 52, Number 3 (2000), 415-429.
First available in Project Euclid: 3 May 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.tmj/1178207821