Tohoku Mathematical Journal
2000
September
SECOND SERIES VOL. 52, NO. 3

Tohoku Math. J.
52 (2000), 415-429

Title MINIMAL MAPS BETWEEN THE HYPERBOLIC DISCS AND GENERALIZED GAUSS MAPS OF MAXIMAL SURFACES IN THE ANTI-DE SITTER 3-SPACE

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

(Received January 6, 1999, revised May 31, 1999)
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.

2000 Mathematics Subject Classification. Primary 58E99; Secondary 58E20, 53C42.

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