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New examples of harmonic diffeomorphisms of the hyperbolic plane onto itself. (English) Zbl 0669.58012
The authors give an explicit construction of a one-parameter family of nonconformal harmonic diffeomorphisms of the hyperbolic plane. They are realized as the Gauss map of spacelike surfaces of revolution of constant mean curvature in the three-dimensional Minkowski space. A description of the boundary behavior of such harmonic maps is also given.
Reviewer: G.Toth
##### MSC:
 5.8e+21 Harmonic maps between infinite-dimensional spaces
##### References:
 [1] K. AKUTAGAWA and S. NISHIKAWA: The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, preprint 1986 [2] R. BARTNIK and L. SIMON: Spacelike hypersurfaces with prescribed boundary values and mean curvature, Commun. Math. Phys.87, 131-152 (1982) · Zbl 0512.53055 · doi:10.1007/BF01211061 [3] H. I. CHOI and A. TREIBERGS: Gauss map of spacelike constant mean curvature hypersurfaces of Minkowski Space, preprint (1988) [4] J. HANO and K. NOMIZU: Surfaces of revolution with constant mean curvature in Lorentz-Minkowski Space, Tôhoku Math. J.,36, 427-437 (1984) · Zbl 0535.53002 · doi:10.2748/tmj/1178228808 [5] J. JOST: Harmonic maps between surfaces, Lecture Notes in Mathematics1062, Berlin Heidelberg New York: Springer-Verlag 1984 [6] T. K. MILNOR: Harmonic maps and classical surface theory in Minkowski Space, Trans. Amer. Math Soc.280, 161-185 (1983) [7] E. RUH and J. VILMS: The tension field of the Gauss map, Trans. Amer. Math. Soc.149, 569-573 (1970) · doi:10.1090/S0002-9947-1970-0259768-5 [8] R. SCHOEN and S.-T. YAU: On univalent harmonic maps between surfaces, Invent. Math.44, 265-278 (1978) · Zbl 0388.58005 · doi:10.1007/BF01403164 [9] A. TREIBERGS: Entire Spacelike Hypersurfaces of constant mean curvature in Minkowski Space, Invent. Math.66, 39-56 (1982) · Zbl 0483.53055 · doi:10.1007/BF01404755