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On finiteness of the number of stable minimal hypersurfaces with a fixed boundary
Author(s):
Frank
Morgan
Journal:
Bull. Amer. Math. Soc.
13
(1985),
133-136.
MSC (1980):
Primary 53C42, 49F22
MathSciNet review:
799795
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Additional information
References:
- [A] Michael T. Anderson, Curvature estimates for minimal surfaces in 3-manifolds, preprint. MR 803196
- [B1] Michael Beeson, Some results on finiteness in Plateau's problem. I, Math. Z. 175 (1980), 103-123. MR 597083
- [B2] Michael Beeson, Some results on finiteness in Plateau's problem. II, Math. Z. 181 (1982), 1-30. MR 671711
- [BT1] R. Böhme and A. J. Tromba, The index theorem for classical minimal surfaces, Ann. of Math. (2) 113 (1981), 447-499. MR 621012
- [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), 1043-1044. MR 461305
- [G] L. Z. Gao, Applications of minimal surface theory to topology and Riemannian geometry, preprint.
- [HS] Robert Hardt and Leon Simon, Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. of Math. (2) 110 (1979), 439-486. MR 554379
- [J] L. P. Jorge, C2 stability of curves with non-degenerate solution to Plateau's problem, Bol. Soc. Brasil. Mat. (to appear). MR 794729
- [K] Miyuki Koiso, On the finite solvability of Plateau's problem for extreme curves, Osaka J. Math. 20 (1983), 177-183. MR 695624
- [L] F.-H. Lin, The Gauss map of a minimal surface, in preparation.
- [Q] Norbert Quien, Über die endliche Lösbarkeit des Plateau-Problems in Riemannischen Manigfaltigkeiten, Manuscripta Math. 39 (1982), 313-338. MR 675548
- [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. 679-695. MR 454874
- [T2] Friedrich Tomi, On the local uniqueness of the problem of least area, Arch. Rational Mech. Anal. 52 (1973), 312-318. 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 m-dimensional surfaces that are stationary for a parametric elliptic integrand, preprint.
- [Wi] H. E. Winkelnkemper, Manifolds as open books, Bull. Amer. Math. Soc. 79 (1973), 45-51. MR 310912
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Additional Information:
DOI:
10.1090/S0273-0979-1985-15396-0
PII:
S 0273-0979(1985)15396-0
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