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Wente, Henry C.

Large solutions to the volume constrained Plateau problem. (English) Zbl 0473.49029

Arch. Ration. Mech. Anal. 75, 59-77 (1980).
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Cited in 2 Reviews
Cited in 50 Documents

MSC:

49Q05 Minimal surfaces and optimization
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
58E12 Variational problems concerning minimal surfaces (problems in two independent variables)

Keywords:

volume constrained Plateau problem; parametric surfaces; solutions in the large; conformal representation of a surface of constant mean curvature; Dirichlet integral; uniform bound on solutions

Citations:

Zbl 0259.53043
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Full Text: DOI

References:

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[14] Steffen, K., Flächen konstanter mittlerer Krümmung mit vorgegebenem Volumen oder Flächeninhalt. Arch. Rational Mech. and Anal.49, 99–128 (1972). · Zbl 0259.53043 · doi:10.1007/BF00281413
[15] Steffen, K., & H. Wente, The Non-existence of Branch Points in Solutions to Certain Classes of Plateau Type Variational Problems. Math. Z. 163, 211–238 (1978). · Zbl 0404.49037 · doi:10.1007/BF01174896
[16] Wente, H., An Existence Theorem for Surfaces of Constant Mean Curvature. Jour. Math. Anal. and Appl. 26, 318–344 (1969). · Zbl 0181.11501 · doi:10.1016/0022-247X(69)90156-5
[17] 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
[18] Wente, H., An Existence Theorem for Surfaces in Equilibrium Satisfying a Volume Constraint, Arch. Rational Mech. and Anal. 50, 139–158(1973). · Zbl 0268.49051 · doi:10.1007/BF00249881
[19] Wente, H., The Differen
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