×

zbMATH — the first resource for mathematics

A general existence theorem for surfaces of constant mean curvature. (English) Zbl 0214.11101

MSC:
49Q99 Manifolds and measure-geometric topics
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Bononcini, V.: Un Teorema di continuita per Integrali su superficie Chiuse. Rivista Mat. Univ. Parma4, 299-311 (1953). · Zbl 0053.03103
[2] Cesari, L.: Surface Area. Ann. Math., No. 35, Princeton, 1956. · Zbl 0073.04101
[3] Courant, R.: Dirichlet’s principle. New York: Wiley (Interscience) 1950. · Zbl 0040.34603
[4] Douglas, J.: Solution of the problem of Plateau. Trans. Amer. Math. Soc.33, 263-321 (1931). · JFM 57.1542.03 · doi:10.1090/S0002-9947-1931-1501590-9
[5] Heinz, E.: Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung. Math. Ann.127, 258-287 (1954). · Zbl 0055.15303 · doi:10.1007/BF01361126
[6] Hildebrandt, S.: On the Plateau problem for surfaces of constant mean curvature. Commun. Pure Appl. Math.23, 97-114 (1970). · Zbl 0181.38703 · doi:10.1002/cpa.3160230105
[7] ?: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendung auf die Kapillaritätstheorie. Math. Z.112, 205-213 (1969). · Zbl 0177.15104 · doi:10.1007/BF01110219
[8] Morrey, C. B.: The problem of Plateau on a Riemannian manifold. Ann. of Math. (2)49, 807-851 (1948). · Zbl 0033.39601 · doi:10.2307/1969401
[9] Morrey, C. B.: Multiple integrals in the calculus of variations. Berlin-Heidelberg-New York: Springer 1966. · Zbl 0142.38701
[10] Osserman, R.: A proof of the regularity everywhere of the classical solution to Plateau’s problem. Ann. of Math. (2)91, 550-569 (1970). · Zbl 0194.22302 · doi:10.2307/1970637
[11] Rado, T.: On the problem of Plateau. Ann. of Math.31, 457-469 (1930). · JFM 56.0437.02 · doi:10.2307/1968237
[12] Wente, H.: An existence theorem for surfaces of constant mean curvature. J. Math. Analysis Appl.26, 318-344 (1969). · Zbl 0181.11501 · doi:10.1016/0022-247X(69)90156-5
[13] Werner, H.: Problem von Douglas für Flächen konstanter mittlerer Krümmung. Math. Ann.135, 303-319 (1957). · Zbl 0077.34901 · doi:10.1007/BF01342884
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.