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On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary. (English) Zbl 0184.32802

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[1] Heinz, E., Über die Existenz einer Fläche konstanter mittlerer Krümmung bei vorgegebener Berandung. Math. Ann. 127, 258–287 (1954). · Zbl 0055.15303
[2] Heinz, E., Über Flächen mit eineindeutiger Projektion auf eine Ebene, deren Krümmungen durch Ungleichungen eingeschränkt sind. Math. Ann. 129, 451–454 (1955). · Zbl 0065.37201
[3] Heinz, E., An inequality of isoperimetric type for surfaces of constant mean curvature. Arch. Rational Mech. Anal. 33, 155–168 (1969). · Zbl 0176.51602
[4] Heinz, E., Ein Regularitätssatz für Flächen beschränkter mittlerer Krümmung. Nachr. Akad. Wiss. Göttingen, Math.-Phys. KI, Jahrgang 1969, 107–118. · Zbl 0192.58302
[5] Hildebrandt, S., Über Flächen konstanter mittlerer Krümmung. Math. Zeitschr., to appear. · Zbl 0183.39501
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[7] Serrin, J., The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Phil. Trans. Royal Soc. London A 264, 413–496 (1969). · Zbl 0181.38003
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[9] Werner, H., Das Problem von Douglas für Flächen konstanter mittlerer Krümmung. Math. Ann. 133, 303–319 (1957). · Zbl 0077.34901
[10] Werner, H., The existence of surfaces of constant mean curvature with arbitrary Jordan curves as assigned boundary. Proc. Amer. Math. Soc. 11, 63–70 (1960). · Zbl 0089.37901
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