×

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


MSC:

58E20 Harmonic maps, etc.
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Courant, R.: Dirichlet’s principle. New York: Interscience Publishers, Inc., 1950 · Zbl 0040.34603
[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) · Zbl 0502.53036
[9] Lemaire, L.: Applications harmonique de surfaces riemanniennes. J. Differential Geometry13 (1), 51-78 (1978) · Zbl 0388.58003
[10] Sacks, J., Uhlenbeck, K.: Minimal surfaces in Riemannian manifolds. Ann. Math. Studies (in press 1982) · Zbl 0527.58008
[11] Sampson, J.: Some properties and applications of harmonic maps. Ann. Sci. École Norm. Sup. (sér 4)11, 211-228 (1978) · Zbl 0392.31009
[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) · Zbl 0132.06004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.