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Harmonic diffeomorphisms between Hadamard manifolds. (English) Zbl 0855.58020
From the authors’ abstract: “In this paper, we study the Dirichlet problem at infinity for harmonic maps between complete hyperbolic Hadamard surfaces. We address the existence and uniqueness questions relating to the problem. In particular, we generalize results in the work of the first two authors [Invent. Math. 105, No. 1, 1-46 (1991; Zbl 0748.58006); Ann. Math., II. Ser. 137, 167-201 (1993; Zbl 0776.58010); Indiana Univ. Math. J. 42, No. 2, 591-635 (1993; Zbl 0790.58011)] and T. Wan [J. Differ. Geom. 35, No. 3, 643-657 (1992; Zbl 0808.53056)]”.
MSC:
58E20Harmonic maps between infinite-dimensional spaces
35K05Heat equation
58J35Heat and other parabolic equation methods for PDEs on manifolds