×

zbMATH — the first resource for mathematics

Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt. (German) Zbl 0259.53043

MSC:
53C40 Global submanifolds
49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Alt, W., Dissertation. Münster 1971.
[2] Courant, R., Dirichlet’s Principle, Conformal Mapping and Minimal Surfaces. New York: Interscience Publ. 1950. · Zbl 0040.34603
[3] Gulliver, R.D., Regularity of minimizing surfaces of prescribed mean curvature. Preprint (1971). · Zbl 0209.24903
[4] Gulliver, R.D., & J. Spruck, The Plateau problem for surfaces of prescribed mean curvature in a cylinder. Invent. math. 13, 169-178 (1971). · Zbl 0214.11103 · doi:10.1007/BF01390099
[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] Heinz, E., An inequality of isoperimetric type for surfaces of constant mean curvature. Arch. Rational Mech. Analysis 33, 155-168 (1969). · Zbl 0176.51602 · doi:10.1007/BF00247758
[7] Heinz, E., Ein Regularitätssatz für Flächen beschränkter mittlerer Krümmung. Nachrichten Akad. Wiss. Göttingen, Math.-Phys. Klasse II, Nr. 12 (1969). · Zbl 0192.58302
[8] Heinz, E., Über das Randverhalten quasilinearer elliptischer Systeme mit isothermen Parametern. Math. Z. 113, 99-105 (1970). · Zbl 0181.11404 · doi:10.1007/BF01141095
[9] Heinz, E., & S. Hildebrandt, The number of branch points of surfaces of bounded mean curvature. J. Differential Geometry 4, 227-235 (1970). · Zbl 0195.23003
[10] Hildebrandt, S., Über Flächen konstanter mittlerer Krümmung. Math. Z. 112, 107-144 (1969). · Zbl 0183.39501 · doi:10.1007/BF01115036
[11] Hildebrandt, S., Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie, I. Math. Z. 112, 205-213 (1969). · Zbl 0177.15104 · doi:10.1007/BF01110219
[12] Hildebrandt, S., On the Plateau problem for surfaces of constant mean curvature. Comm. Pure Appl. Math. 23, 97-114 (1970). · Zbl 0181.38703 · doi:10.1002/cpa.3160230105
[13] Hildebrandt, S., Einige Bemerkungen über Flächen beschränkter mittlerer Krümmung. Math. Z. 115, 169-178 (1970). · Zbl 0191.20504 · doi:10.1007/BF01109855
[14] Hildebrandt, S., Über einen neuen Existenzsatz für Flächen vorgeschriebener mittlerer Krümmung. Math. Z. 119, 267-272 (1971). · Zbl 0204.21703 · doi:10.1007/BF01113400
[15] Jäger, W., Remarks on results of Heinz concerning the continuity of total variations. Arch. Rational Mech. Analysis 37, 21-28 (1970). · Zbl 0201.13802
[16] Morrey, C.B., On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 43, 126-166 (1938). · Zbl 0018.40501 · doi:10.1090/S0002-9947-1938-1501936-8
[17] Morrey, C.B., Multiple integral problems in the calculus of variations and related topics. Univ. California Publ. Math., New Ser. 1, No. 1, 1-130 (1943). · Zbl 0063.04107
[18] Morrey, C.B., The problem of Plateau on a Riemannian manifold. Ann. of Math. 49, 807-851 (1949). · Zbl 0033.39601 · doi:10.2307/1969401
[19] Morrey, C.B., Multiple Integrals in the Calculus of Variations. Berlin-Heidelberg-New York: Springer 1966. · Zbl 0142.38701
[20] Nitsche, J.C.C., On new results in the theory of minimal surfaces. Bull. Amer. Math. Soc. 71, 195-270 (1965). · Zbl 0135.21701 · doi:10.1090/S0002-9904-1965-11276-9
[21] Nitsche, J.C.C., Contours bounding at least three solutions of Plateau’s problem. Arch. Rational Mech. Analysis 30, 1-11 (1968). · Zbl 0164.14201
[22] Steffen, K., Existenzsätze für Flächen konstanter mittlerer Krümmung mit vorgegebener Randkurve. Dissertation, Mainz 1971.
[23] Steffen, K., Ein verbesserter Existenzsatz für Flächen konstanter mittlerer Krümmung. Manuscripta Math. 6, 105-139 (1972). · Zbl 0229.53011 · doi:10.1007/BF01369709
[24] 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
[25] 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
[26] Werner, H., Das Problem von Douglas für Flächen konstanter mittlerer Krümmung. Math. Ann. 133, 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.