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Steffen, Klaus

On the existence of surfaces with prescribed mean curvature and boundary. (English) Zbl 0343.49016

Math. Z. 146, 113-135 (1976).
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Cited in 19 Documents

MSC:

49Q20 Variational problems in a geometric measure-theoretic setting
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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References:

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[3] Federer, H.: Geometric measure theory. Berlin-Heidelberg-New York: Springer 1969 · Zbl 0176.00801
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[10] Heinz, E.: On the nonexistence of a surface of constant mean curvature with finite area and prescribed rectifiable boundary. Arch. rat. Mech. Analysis35, 249-252 (1969) · Zbl 0184.32802 · doi:10.1007/BF00248159
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[13] Hildebrandt, S.: On the Plateau problem for surfaces of constant mean curvature. Commun. pure appl. Math.23, 97-114 (1970) · Zbl 0181.38703 · doi:10.1002/cpa.3160230105
[14] Hildebrandt, S.: Randwertprobleme für Flächen vorgeschriebener mittlerer Krümmung und Anwendungen auf die Kapillaritätstheorie. Math. Z.112, 205-213 (1969) · doi:10.1007/BF01110219
[15] Hildebrandt, S.: Einige Bemerkungen über Flächen beschränkter mittlerer Krümmung. Math. Z.115, 169-178 (1970) · doi:10.1007/BF01109855
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[17] Hildebrandt, S., Kaul, H.: Two-dimensional variational problems with obstructions and Plateau’s problem forH-surfaces in a Riemannian manifold. Commun. pure appl. Math.25, 187-223 (1972) · Zbl 0245.53006 · doi:10.1002/cpa.3160250208
[18] Osserman, R.: A proof of the regularity everywhere of the classical solution to Plateau’s problem. Annals of Math., II. Ser.91, 550-563 (1970) · Zbl 0194.22302 · doi:10.2307/1970637
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[21] Steffen, K.: Isoperimetric inequalities and the problem of Plateau. Preprint. · Zbl 0345.49024
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