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Uniqueness of harmonic mappings and of solutions of elliptic equations on Riemannian manifolds

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References

  1. Bishop, R. L., Crittenden, R.J.: Geometry of manifolds. New York, London: Academic Press 1964

    Google Scholar 

  2. Heinz, E.: Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgeschriebener Berandung. Math. Ann.127, 258–287 (1954)

    Google Scholar 

  3. Heinz, E., Tomi, F.: Zu einem Satz von Hildebrandt über das Randverhalten von Minimalflächen. Math. Z.111, 372–386 (1969)

    Google Scholar 

  4. Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Großen. Berlin, Heidelberg. New York: Springer 1968

    Google Scholar 

  5. Gulliver, R.D.: The Plateau problem for surfaces of prescribed mean curvature in a Riemannian manifold. J. Diff. Geom.8, 317–330 (1973)

    Google Scholar 

  6. Hamilton, R.S.: Harmonic maps of manifolds with boundary. Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer 1975

    Google Scholar 

  7. Hildebrandt, S., Kaul, H.: Two-dimensional variational problems with obstructions, and Plateau's problem forH-surfaces in a Riemannian manifold. Comm. Pure Appl. Math.25, 187–223 (1972)

    Google Scholar 

  8. Hildebrandt, S., Kaul, H., Widman, K.-O.: An existence theorem for harmonic mappings of Riemannian manifolds. Acta Math.138, 1–16 (1977)

    Google Scholar 

  9. Jäger, W.: Ein Maximumprinzip für ein System nichtlinearer Differentialgleichungen. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II.11, (1976)

  10. Karcher, H.: Riemann center of mass and mollifier smoothing. Comm. Pure Appl. Math.30, 509–541 (1977)

    Google Scholar 

  11. Kaul, H.: Das Dirichletproblem für elliptische Differentialoperatoren mit Variationsstruktur auf Riemannschen Mannigfaltigkeiten. Bonn. Math. Schr.94 (1977)

  12. Morrey, C.B.: The problem of Plateau on a Riemannian manifold. Ann. of Math.49, 807–851 (1948)

    Google Scholar 

  13. Stampacchia, G.: On some regular multiple integral problems in the calculus of variations. Comm. Pure Appl. Math.16, 383–421 (1963)

    Google Scholar 

  14. Steffen, K.: Ein verbesserter Existenzsatz für Flächen konstanter mittlerer Krümmung. manuscripta math.6, 105–139 (1972)

    Google Scholar 

  15. Wahl, W.v.: Existenzsätze für nichtlineare elliptische Systeme. Nachr. Akad. Wiss. Göttingen, Jg. 1978, Heft 3

  16. Wente, H.: An existence theorem for surfaces of constant mean curvature. J. Math. Anal. Appl.26, 318–344 (1969)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Im Neuenheimer Feld 294, D-6900, Heidelberg, Federal Republic of Germany

    Willi Jäger

  2. Fachbereich Mathematik der Universität Tübingen, Auf der Morgenstelle 10, D-7400, Tübingen, Federal Republic of Germany

    Helmut Kaul

Authors
  1. Willi Jäger
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  2. Helmut Kaul
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Additional information

The work of the secondly-named author was supported by the Sonderforschungsbereich Theoretische Mathematik at the University of Bonn

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Jäger, W., Kaul, H. Uniqueness of harmonic mappings and of solutions of elliptic equations on Riemannian manifolds. Math. Ann. 240, 231–250 (1979). https://doi.org/10.1007/BF01362313

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