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Large solutions to the volume constrained plateau problem

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Bibliography

  1. Alt, W., Verzweigungspunkte von H-Flächen. Math. Z. 127, 333–362 (1972)

    Google Scholar 

  2. Bononcini, V., Un Teorema di Continuita per Integrali su Superficie Chisue. Riv. Math. U. Parma 4, 299–311 (1953)

    Google Scholar 

  3. Courant, R., Dirichlet's Principle. New York: Wiley (Interscience) 1950

    Google Scholar 

  4. Douglas, J., Solution of the Problem of Plateau. Trans. Am. Math. Soc. 33, 263–321 (1931)

    Google Scholar 

  5. Gulliver, R., Regularity of Minimizing Surfaces of Prescribed Mean Curvature. Ann. of Math. 97, 275–305 (1973).

    Google Scholar 

  6. scGulliver, R., Removability of Singular Points on Surfaces of Mean Curvature. J. of Diff.Geom. II, 345–350 (1976).

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

    Google Scholar 

  8. Heinz, E., An Inequality of Isoperimetric Type for Surfaces of Constant Mean Curvature. Arch. Rational Mech. and Anal. 23, 155–168 (1969).

    Google Scholar 

  9. Jäger, W., Remarks on Results of Heinz concerning the Continuity of Total Variations. Arch. Rational Mech. and Anal. 37, 21–28(1970).

    Google Scholar 

  10. Morrey, C., Multiple Integrals in the Calculus of Variations. New York: Springer1966.

    Google Scholar 

  11. Osserman, R., A Proof of the Regularity Everywhere of the Classical Solution to Plateau's Problem. Ann. of Math. 91, 550–569 (1970).

    Google Scholar 

  12. Rado, T., On the Problem of Plateau. Ann. of Math. 31, 457–469(1930).

    Google Scholar 

  13. Serrin, J., On surfaces of Constant Mean Curvature which Span a Given Space Curve. Math. Z.112, 77–88(1969).

    Google Scholar 

  14. Steffen, K., Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt. Arch. Rational Mech. and Anal.49, 99–128 (1972).

    Google Scholar 

  15. Steffen, K., & H. Wente, The Non-existence of Branch Points in Solutions to Certain Classes of Plateau Type Variational Problems. Math. Z. 163, 211–238 (1978).

    Google Scholar 

  16. Wente, H., An Existence Theorem for Surfaces of Constant Mean Curvature. Jour. Math. Anal. and Appl. 26, 318–344 (1969).

    Google Scholar 

  17. Wente, H., A General Existence Theorem for Surfaces of Constant Mean Curvature. Math. Z. 120, 277–288 (1971).

    Google Scholar 

  18. Wente, H., An Existence Theorem for Surfaces in Equilibrium Satisfying a Volume Constraint, Arch. Rational Mech. and Anal. 50, 139–158(1973).

    Google Scholar 

  19. Wente, H., The Differential Equation Δx = 2H(x u.xv) with Vanishing Boundary Values, Poc.A.M.S. 50, 131–137 (1975).

    Google Scholar 

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Communicated by J. C. C. Nitsche

The author was partially supported by a grant from the National Science Foundation. The work was completed while the author was on sabbatical leave visiting the University of Minnesota, Stanford University, and the University of Bonn.

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Wente, H.C. Large solutions to the volume constrained plateau problem. Arch. Rational Mech. Anal. 75, 59–77 (1980). https://doi.org/10.1007/BF00284621

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