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On the existence of harmonic diffeomorphisms between surfaces. (English) Zbl 0488.58009

MSC:
58E20Harmonic maps between infinite-dimensional spaces
58E05Abstract critical point theory
References:
[1]Courant, R.: Dirichlet’s principle. New York: Interscience Publishers, Inc., 1950
[2]Eells, J., Lemaire, L.: A report on harmonic maps. Bull. London Math. Soc.10, 1-68 (1978) · Zbl 0401.58003 · doi:10.1112/blms/10.1.1
[3]Heinz, E.: Über das Nichtverschwinden der Funktionaldeterminante bei einer Klasse eindeutiger Abbildungen. Math. Z.105, 87-89 (1968) · Zbl 0159.40203 · doi:10.1007/BF01110433
[4]Hildebrandt, S., Jost, J., Widman, K.O.: Harmonic mappings and minimal submanifolds. Invent. Math.62, 269-298 (1980) · Zbl 0446.58006 · doi:10.1007/BF01389161
[5]Hildebrandt, S., Kaul, H., Widman, K.O.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math.138, 1-16 (1977) · Zbl 0356.53015 · doi:10.1007/BF02392311
[6]Jäger, K., Kaul, H.: Uniqueness and stability of harmonic maps and their Jacobi fields. Manuscripta Math.28 (4). 269-291 (1979) · Zbl 0413.31006 · doi:10.1007/BF01647975
[7]Jost, J.: Univalency of harmonic maps between surfaces. J. Reine Angew. Math.324, 141-153 (1981) · Zbl 0453.53036 · doi:10.1515/crll.1981.324.141
[8]Jost, J., Karcher, H.: Einigea-Priori Abschätzungen für harmonische Abbildungen. (in press 1982)
[9]Lemaire, L.: Applications harmonique de surfaces riemanniennes. J. Differential Geometry13 (1), 51-78 (1978)
[10]Sacks, J., Uhlenbeck, K.: Minimal surfaces in Riemannian manifolds. Ann. Math. Studies (in press 1982)
[11]Sampson, J.: Some properties and applications of harmonic maps. Ann. Sci. École Norm. Sup. (sér 4)11, 211-228 (1978)
[12]Schoen, R., Yau, S.T.: On univalent harmonic maps between surfaces. Invent. Math.44, 265-278 (1978) · Zbl 0388.58005 · doi:10.1007/BF01403164
[13]Schoen, R., Yau, S.T.: Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Ann. Math.110, 127-142 (1979) · Zbl 0431.53051 · doi:10.2307/1971247
[14]Shibata, K.: On the existence of a harmonic mapping. Osaka J. Math.15, 173-211 (1963)