References
Alexandroff, A. D., A characteristic property of spheres, Annali di Mat. (1962), 203–315.
Alt, H. W., Verzweigungspunkte von H-Flächen, Math. Z. 127 (1972), 333–362.
Ambrosetti, A., & P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349–381.
Barbosa, J. L., & M. do Carmo, Hopf's conjecture for stable immersed surfaces, preprint.
Bononcini, V., Un teorema di continuitá per integrali su superficie chiuse, Riv. Mat. Univ. Parma 4 (1953), 299–311.
Courant, R., Dirichlet's principle, conformal mapping and minimal surfaces, Interscience, New York 1950.
Dierkes, U., Hildebrandt, S., & O. Wohlrab, Minimalflächen, to appear.
Douglas, J., Solution of the problem of Plateau, Trans. A.M.S.33 (1931), 263–321.
Douglas, J., Minimal surfaces of higher topological structure, Annals of Math. 40 (1939), 205–298.
Heinz, E., Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung, Math. Ann. 127 (1954), 258–287.
Heinz, E., On the existence problem for surfaces of constant mean curvature, Comm. Pure Math. 9 (1956), 467–470.
Heinz, E., An inequality of isoperimetric type for surfaces of constant mean curvature, Arch. Rational Mech. Anal. 33 (1969), 155–168.
Heinz, E., On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary, Arch. Rational Mech. Anal. 35 (1969), 249–252.
Heinz, E., Unstable surfaces of constant mean curvature, Arch. Rational Mech. Anal. 38 (1970), 257–267.
Hildebrandt, S., Boundary behaviour of minimal surfaces, Arch. Rational Mech. Anal. 35 (1969), 47–69.
Hildebrandt, S., Über das Randverhalten von Minimalflächen, Math. Ann. 165 (1966), 1–18.
Hildebrandt, S., Über Flächen konstanter mittlerer Krümmung, Math. Z. 112 (1969), 107–144.
Hildebrandt, S., Randwertprobleme für Flächen vorgeschriebenen mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie, Math. Z. 112 (1969), 205–213.
Hildebrandt, S., On the Plateau problem for surfaces of constant mean curvature, Comm. Pure Appl. Math. 23 (1970), 97–114.
Hildebrandt, S., Nonlinear elliptic systems and harmonic mappings, SFB-Vorlesungsreihe no. 3, University of Bonn, 1980.
Hopf, H., Über Flächen mit einer Relation zwischen den Hauptkrümmungen, Math. Nachr. 4 (1951), 239–249.
Morrey, C. B., Multiple integrals in the calculus of variations, Springer, Berlin, Heidelberg, New York, 1966.
Morse, M., & C. B. Tompkins, The existence of minimal surfaces of general critical types, Ann. of Math. (2) 40 (1939), 443–472, and 42 (1941), 331.
Nitsche, J. C. C., Vorlesungen über Minimalflächen, Springer, Berlin-Heidelberg-New York, 1976.
Palais, R. S., & S. Smale, A generalized Morse theory, Bull. A.M.S. 70 (1964), 165–171.
Radó, T., On the problem of Plateau, Ann. of Math. 31 (1930), 457–469.
Serrin, J., On surfaces of constant mean curvature that span a given space curve, Math. Z. 112 (1969), 77–88.
Shiffman, M., The Plateau problem for nonrelative minima, Ann. of Math. (2) 40(1939), 834–854.
Steffen, K., Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt, Arch. Rational Mech. Anal. 49 (1972), 99–128.
Steffen, K., Ein verbesserter Existenzsatz für Flächen konstanter mittlerer Krümmung, Manusc. Math. 6 (1972), 105–139.
Steffen, K., Isoperimetric inequalities and the problem of Plateau, Math. Ann.222 (1976), 97–144.
Ströhmer, G., Instabile Flächen vorgeschriebener mittlerer Krümmung, Math. Z. 174 (1980), 119–133.
Struwe, M., Multiple solutions of differential equations without the Palais-Smale condition, Math. Ann. 261 (1982), 399–412.
Struwe, M., Quasilinear elliptic eigenvalue problems, Comm, Math. Helv. 58 (1983), 509–527.
Tomi, F., Bemerkungen zum Regularitätsproblem der Gleichung vorgeschriebenen mittlerer Krümmung, Math. Z. 132 (1973), 323–326.
Wente, H., An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl. 26 (1969), 318–344.
Wente, H., A general existence theorem for surfaces of constant mean curvature, Math. Z. 120 (1971), 277–288.
Wente, H., The differential equation Δx = 2Hx u ∧ xv with vanishing boundary values, Proc. A.M.S. 50 (1975), 131–137.
Wente, H., Large solutions to the volume constrained Plateau problem, Arch. Rational Mech. Anal. 75 (1980), 59–77.
Wente, H., in Analysis-Seminar 1981, SFB-Vorlesungsreihe no. 8, Univ. of Bonn, 1981.
Werner, H., Das Problem von Douglas für Flächen konstanter mittlerer Krümmung, Math. Ann. 133 (1957), 303–319.
Author information
Authors and Affiliations
Additional information
Communicated by J. C. C. Nitsche
Rights and permissions
About this article
Cite this article
Struwe, M. Nonuniqueness in the plateau problem for surfaces of constant mean curvature. Arch. Rational Mech. Anal. 93, 135–157 (1986). https://doi.org/10.1007/BF00279957
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00279957