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On the area of harmonic surfaces. (English) Zbl 0358.53001

MSC:

53A05 Surfaces in Euclidean and related spaces
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References:

[1] Emilio Baiada, L’area delle superficie armoniche quale funzione delle rappresentazioni del contorno, Rivista Mat. Univ. Parma 2 (1951), 315 – 330 (Italian). · Zbl 0044.28102
[2] M. Beeson, Plateau’s problem and constructive mathematics (to appear). · Zbl 0452.03046
[3] Michael J. Beeson, Principles of continuous choice and continuity of functions in formal systems for constructive mathematics, Ann. Math. Logic 12 (1977), no. 3, 249 – 322. · Zbl 0393.03012 · doi:10.1016/S0003-4843(77)80003-X
[4] R. Courant, Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces, Interscience Publishers, Inc., New York, N.Y., 1950. Appendix by M. Schiffer. · Zbl 0040.34603
[5] Erhard Heinz, Unstable surfaces of constant mean curvature, Arch. Rational Mech. Anal. 38 (1970), 257 – 267. · Zbl 0203.53804 · doi:10.1007/BF00281523
[6] Marston Morse and C. Tompkins, The continuity of the area of harmonic surfaces as a function of the boundary representations, Amer. J. Math. 63 (1941), 825 – 838. · Zbl 0026.12404 · doi:10.2307/2371624
[7] Johannes C. C. Nitsche, Vorlesungen über Minimalflächen, Springer-Verlag, Berlin-New York, 1975 (German). Die Grundlehren der mathematischen Wissenschaften, Band 199. · Zbl 0319.53003
[8] Max Shiffman, Unstable minimal surfaces with any rectifiable boundary, Proc. Nat. Acad. Sci. U. S. A. 28 (1942), 103 – 108. · Zbl 0063.06962
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