×

zbMATH — the first resource for mathematics

Large solutions to the volume constrained Plateau problem. (English) Zbl 0473.49029

MSC:
49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
58E12 Variational problems concerning minimal surfaces (problems in two independent variables)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alt, W., Verzweigungspunkte von H-Flächen. Math. Z. 127, 333–362 (1972) · Zbl 0253.58007 · doi:10.1007/BF01111392
[2] Bononcini, V., Un Teorema di Continuita per Integrali su Superficie Chisue. Riv. Math. U. Parma 4, 299–311 (1953)
[3] Courant, R., Dirichlet’s Principle. New York: Wiley (Interscience) 1950 · Zbl 0040.34603
[4] Douglas, J., Solution of the Problem of Plateau. Trans. Am. Math. Soc. 33, 263–321 (1931) · Zbl 0001.14102 · doi:10.1090/S0002-9947-1931-1501590-9
[5] Gulliver, R., Regularity of Minimizing Surfaces of Prescribed Mean Curvature. Ann. of Math. 97, 275–305 (1973). · Zbl 0246.53053 · doi:10.2307/1970848
[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). · Zbl 0055.15303 · doi:10.1007/BF01361126
[8] Heinz, E., An Inequality of Isoperimetric Type for Surfaces of Constant Mean Curvature. Arch. Rational Mech. and Anal. 23, 155–168 (1969). · Zbl 0176.51602 · doi:10.1007/BF00247758
[9] Jäger, W., Remarks on Results of Heinz concerning the Continuity of Total Variations. Arch. Rational Mech. and Anal. 37, 21–28(1970). · Zbl 0201.13802 · doi:10.1007/BF00249498
[10] Morrey, C., Multiple Integrals in the Calculus of Variations. New York: Springer1966. · Zbl 0142.38701
[11] Osserman, R., A Proof of the Regularity Everywhere of the Classical Solution to Plateau’s Problem. Ann. of Math. 91, 550–569 (1970). · Zbl 0194.22302 · doi:10.2307/1970637
[12] Rado, T., On the Problem of Plateau. Ann. of Math. 31, 457–469(1930). · JFM 56.0437.02 · doi:10.2307/1968237
[13] Serrin, J., On surfaces of Constant Mean Curvature which Span a Given Space Curve. Math. Z.112, 77–88(1969). · Zbl 0182.24001 · doi:10.1007/BF01115033
[14] Steffen, K., Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt. Arch. Rational Mech. and Anal.49, 99–128 (1972). · Zbl 0259.53043 · doi:10.1007/BF00281413
[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). · Zbl 0404.49037 · doi:10.1007/BF01174896
[16] Wente, H., An Existence Theorem for Surfaces of Constant Mean Curvature. Jour. Math. Anal. and Appl. 26, 318–344 (1969). · Zbl 0181.11501 · doi:10.1016/0022-247X(69)90156-5
[17] Wente, H., A General Existence Theorem for Surfaces of Constant Mean Curvature. Math. Z. 120, 277–288 (1971). · Zbl 0214.11101 · doi:10.1007/BF01117500
[18] Wente, H., An Existence Theorem for Surfaces in Equilibrium Satisfying a Volume Constraint, Arch. Rational Mech. and Anal. 50, 139–158(1973). · Zbl 0268.49051 · doi:10.1007/BF00249881
[19] Wente, H., The Differen
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.