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Böhme, R.; Tromba, A. J.

The number of solutions to the classical Plateau problem is generically finite. (English) Zbl 0369.49020

Bull. Am. Math. Soc. 83, 1043-1044 (1977).
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Cited in 2 Documents

MSC:

49Q05 Minimal surfaces and optimization
58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
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References:

[1] Reinhold Böhme, Stability of minimal surfaces, Function theoretic methods for partial differential equations (Proc. Internat. Sympos., Darmstadt, 1976) Springer, Berlin, 1976, pp. 123 – 137. Lecture Notes in Math., Vol. 561. Reinhold Böhme, Über Stabilität und Isoliertheit der Lösungen des klassischen Plateauproblems, Math. Z. 158 (1978), no. 3, 211 – 243 (German). · Zbl 0396.53004 · doi:10.1007/BF01214794
[2] 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
[3] Jesse Douglas, Solution of the problem of Plateau, Trans. Amer. Math. Soc. 33 (1931), no. 1, 263 – 321. · Zbl 0001.14102
[4] Erhard Heinz and Friedrich Tomi, Zu einem Satz von Hildebrandt über das Randverhalten von Minimalflächen, Math. Z. 111 (1969), 372 – 386 (German). · Zbl 0172.38601 · doi:10.1007/BF01110748
[5] Stefan Hildebrandt, Boundary behavior of minimal surfaces, Arch. Rational Mech. Anal. 35 (1969), 47 – 82. · Zbl 0183.39402 · doi:10.1007/BF00248494
[6] Johannes C. C. Nitsche, The boundary behavior of minimal surfaces. Kellogg’s theorem and Branch points on the boundary, Invent. Math. 8 (1969), 313 – 333. , https://doi.org/10.1007/BF01404636 Johannes C. C. Nitsche, Concerning my paper on the boundary behavior of minimal surfaces, Invent. Math. 9 (1969/1970), 270. · Zbl 0202.20601 · doi:10.1007/BF01404330
[7] Tibor Radó, On the problem of Plateau. Subharmonic functions, Springer-Verlag, New York-Heidelberg, 1971. Reprint. · Zbl 0211.13803
[8] Friedrich Tomi, Ein einfacher Beweis eines Regularitässatzes für schwache Lösungen gewisser elliptischer Systeme, Math. Z. 112 (1969), 214 – 218 (German). · Zbl 0177.14704 · doi:10.1007/BF01110220
[9] A. J. Tromba, On the number of solutions to Plateau’s problem, Bull. Amer. Math. Soc. 82 (1976), no. 1, 66 – 68. · Zbl 0316.35027
[10] A. J. Tromba, On the number of simply connected minimal surfaces spanning a curve, Mem. Amer. Math. Soc. 12 (1977), no. 194, v+121. · Zbl 0389.53003 · doi:10.1090/memo/0194
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