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The Plateau problem for surfaces of prescribed mean curvature in a cylinder. (English) Zbl 0214.11103


MSC:

49Q99 Manifolds and measure-geometric topics
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References:

[1] Courant, R.: Dirichlet’s principle, conformal mapping, and minimal surfaces. New York: Interscience 1950. · Zbl 0040.34603
[2] Gulliver, R.: On regularity of generalized surfaces of constant mean curvature. Bull A.M.S.77, 243-246 (1971). · Zbl 0209.24903 · doi:10.1090/S0002-9904-1971-12700-3
[3] 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
[4] Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritästheorie I. Math. Z.112, 205-213 (1969). · Zbl 0177.15104 · doi:10.1007/BF01110219
[5] ? 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
[6] Serrin, J.: Or the Dirichlet problem for surfaces of constant mean curvature (to appear). · Zbl 0199.16604
[7] Tomi, F.: Ein einfacher Beweis eines Regularitätssatzes für schwache Lösungen gewisser elliptischer Systeme. Math. Z.112, 214-218 (1969). · Zbl 0177.14704 · doi:10.1007/BF01110220
[8] Wente, H.: An existence theorem for surfaces of constant mean curvature. J. Math. Anal. Appl.26, 318-344 (1969). · Zbl 0181.11501 · doi:10.1016/0022-247X(69)90156-5
[9] Heinz, E.: On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary. Arch. Rational Mech. Anal.35, 249-250 (1969). · Zbl 0184.32802 · doi:10.1007/BF00248159
[10] Hildebrandt, S.: Über einen neuen Existenzsatz für Flächen vorgeschriebener mittlerer Krümmung (preprint). · Zbl 0202.20501
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