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On the nonexistence of a hypersurface of prescribed mean curvature with a given boundary. (English) Zbl 0266.53002

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
49Q05 Minimal surfaces and optimization
35J67 Boundary values of solutions to elliptic equations and elliptic systems
53C40 Global submanifolds
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References:
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[11] Heinz, E.: Über das Randverhalten quasilinearer elliptischer Systeme mit isothermen Parametern. Math. Z.113, 99-105 (1970) · Zbl 0181.11404
[12] Hildebrandt, S.: Randwertprobleme für Flächen mit vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie I. Math. Z.112, 205-213 (1969) · Zbl 0177.15104
[13] Hildebrandt, S., Kaul, H.: Two-dimensional variational problems with obstructions, and Plateau’s problem for H-surfaces in a Riemannian manifold. Comm. Pure Appl. Math.25, 187-223 (1972) · Zbl 0245.53006
[14] Katsurada, Y.: On a piece of hypersurface in a Riemannian manifold with mean curvature bounded away from zero. Trans. Amer. Math. Soc.129, 447-457 · Zbl 0172.46804
[15] Serrin, J.: The problem of Dirichlet for quasilinear elliptic differential equations with many independent variables. Phil. Trans. Royal Soc. London (Ser.A)264, 413-496 (1969) · Zbl 0181.38003
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