On finiteness of the number of stable minimal hypersurfaces with a fixed boundary
Author:
Frank Morgan
Journal:
Bull. Amer. Math. Soc. 13 (1985), 133136
MSC (1980):
Primary 53C42, 49F22
DOI:
https://doi.org/10.1090/S027309791985153960
MathSciNet review:
799795
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References  Similar Articles  Additional Information
 Michael T. Anderson, Curvature estimates for minimal surfaces in 3manifolds, Ann. Sci. École Norm. Sup. (4) 18 (1985), no. 1, 89–105. MR 803196
 Michael Beeson, Some results on finiteness in Plateau’s problem. I, Math. Z. 175 (1980), no. 2, 103–123. MR 597083, https://doi.org/10.1007/BF01674441
 Michael Beeson, Some results on finiteness in Plateau’s problem. II, Math. Z. 181 (1982), no. 1, 1–30. MR 671711, https://doi.org/10.1007/BF01214978
 R. Böhme and A. J. Tromba, The index theorem for classical minimal surfaces, Ann. of Math. (2) 113 (1981), no. 3, 447–499. MR 621012, https://doi.org/10.2307/2006993

[BT2] R. Böhme and A. J. Tromba, The number of solutions to the classical Plateau problem is generally finite, Bull. Amer. Math. Soc. 83 (1977), 10431044. MR 461305

[G] L. Z. Gao, Applications of minimal surface theory to topology and Riemannian geometry, preprint.
 Robert Hardt and Leon Simon, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. (2) 110 (1979), no. 3, 439–486. MR 554379, https://doi.org/10.2307/1971233
 L. P. Jorge, 𝐶² stability of curves with nondegenerate solution to Plateau’s problem, Bol. Soc. Brasil. Mat. 15 (1984), no. 12, 55–84. MR 794729, https://doi.org/10.1007/BF02584708
 Miyuki Koiso, On the finite solvability of Plateau’s problem for extreme curves, Osaka J. Math. 20 (1983), no. 1, 177–183. MR 695624

[L] F.H. Lin, The Gauss map of a minimal surface, in preparation.
 Norbert Quien, Über die endliche Lösbarkeit des PlateauProblems in Riemannschen Mannigfaltigkeiten, Manuscripta Math. 39 (1982), no. 23, 313–338 (German, with English summary). MR 675548, https://doi.org/10.1007/BF01165795

[T1] Friedrich Tomi, On the finite solvability of Plateau's problem, Geometry and Topology, Lecture Notes in Math., vol. 597, Springer, New York, 1977, pp. 679695. MR 454874

[T2] Friedrich Tomi, On the local uniqueness of the problem of least area, Arch. Rational Mech. Anal. 52 (1973), 312318. MR 346639

[Tr] A. J. Tromba, On the number of minimal surfaces spanning a wire, Mem. Amer. Math. Soc. No. 194 (1977). MR 649458

[W] Brian White, The space of mdimensional surfaces that are stationary for a parametric elliptic integrand, preprint.

[Wi] H. E. Winkelnkemper, Manifolds as open books, Bull. Amer. Math. Soc. 79 (1973), 4551. MR 310912
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Additional Information
DOI:
https://doi.org/10.1090/S027309791985153960