Harmonic diffeomorphisms between Hadamard manifolds

Li, Peter; Tam, Luen-Fai; Wang, Jiaping

doi:10.1090/S0002-9947-1995-1308017-2

Harmonic diffeomorphisms between Hadamard manifolds
HTML articles powered by AMS MathViewer

by Peter Li, Luen-Fai Tam and Jiaping Wang

Trans. Amer. Math. Soc. 347 (1995), 3645-3658

DOI: https://doi.org/10.1090/S0002-9947-1995-1308017-2

PDF | Request permission

Abstract:

In this paper, we study the Dirichlet problem at infinity for harmonic maps between complete hyperbolic Hadamard surfaces. We will address the existence and uniqueness questions relating to the problem. In particular, we generalize results in the work of Li-Tam and Wan.

References

Kazuo Akutagawa, Harmonic diffeomorphisms of the hyperbolic plane, Trans. Amer. Math. Soc. 342 (1994), no. 1, 325–342. MR 1147398, DOI 10.1090/S0002-9947-1994-1147398-9
Hyeong In Choi and Andrejs Treibergs, Gauss maps of spacelike constant mean curvature hypersurfaces of Minkowski space, J. Differential Geom. 32 (1990), no. 3, 775–817. MR 1078162
S. Y. Cheng and S. T. Yau, Differential equations on Riemannian manifolds and their geometric applications, Comm. Pure Appl. Math. 28 (1975), no. 3, 333–354. MR 385749, DOI 10.1002/cpa.3160280303
David Gilbarg and Neil S. Trudinger, Elliptic partial differential equations of second order, Grundlehren der Mathematischen Wissenschaften, Vol. 224, Springer-Verlag, Berlin-New York, 1977. MR 0473443
Peter Li and Luen-Fai Tam, The heat equation and harmonic maps of complete manifolds, Invent. Math. 105 (1991), no. 1, 1–46. MR 1109619, DOI 10.1007/BF01232256
Peter Li and Luen-Fai Tam, Uniqueness and regularity of proper harmonic maps, Ann. of Math. (2) 137 (1993), no. 1, 167–201. MR 1200080, DOI 10.2307/2946622
Peter Li and Luen-Fai Tam, Uniqueness and regularity of proper harmonic maps. II, Indiana Univ. Math. J. 42 (1993), no. 2, 591–635. MR 1237061, DOI 10.1512/iumj.1993.42.42027
Richard M. Schoen, The role of harmonic mappings in rigidity and deformation problems, Complex geometry (Osaka, 1990) Lecture Notes in Pure and Appl. Math., vol. 143, Dekker, New York, 1993, pp. 179–200. MR 1201611
Tom Yau-Heng Wan, Constant mean curvature surface, harmonic maps, and universal Teichmüller space, J. Differential Geom. 35 (1992), no. 3, 643–657. MR 1163452
Shing Tung Yau, A general Schwarz lemma for Kähler manifolds, Amer. J. Math. 100 (1978), no. 1, 197–203. MR 486659, DOI 10.2307/2373880