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Minimal surfaces bounded by a pair of convex planar curves
Author(s):
William H.
Meeks III;
Brian
White
Journal:
Bull. Amer. Math. Soc.
24
(1991),
179-184.
MSC (1985):
Primary 53A10, 49F10;
Secondary 58E12
MathSciNet review:
1069989
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Additional information
References:
- 1.
- J. L. Barbosa and M. do Carmo, On the size of a stable minimal surface in R3 , Amer. J. Math. 19(8) (1976), 515-528. MR 413172
- 2.
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- 3.
- D. Hoffman, H. Rosenberg, and J. Spruck, personal communication.
- 4.
- W. H. Meeks III and B. White, Minimal surfaces bounded by convex curves in parallel planes, Comment. Math. Helv. (to appear). MR 1107841
- 5.
- W. H. Meeks III and B. White, The space of minimal annuli bounded by an extremal pair of planar curves, preprint.
- 6.
- W. H. Meeks III and S. T. Yau, The existence of embedded minimal surfaces and the problem of uniqueness, Math. Z. 179 (1982), 151-168. MR 645492
- 7.
- B. Riemann, Ouevres mathématiques de Riemann, Gauthiers-Villars, Paris, 1898.
- 8.
- R. Schoen, Uniqueness, symmetry, and embeddedness of minimal surfaces, J. Differential Geom. 18 (1983), 791-809. MR 730928
- 9.
- M. Shiffman, On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes, Ann. of Math. (2) 63 (1956), 77-90. MR 74695
- 10.
- S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. Math. 87(1965), 861-866. MR 185604
- 11.
- F. Tomi and A. J. Tromba, Extreme curves bound an embedded minimal surface of disk type, Math. Z. 158 (1978), 137-145. MR 486522
- 12.
- B. White, New applications of mapping degrees to minimal surface theory, J. Differential Geom. 29 (1989), 143-162. MR 978083
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Additional Information:
DOI:
10.1090/S0273-0979-1991-15983-5
PII:
S 0273-0979(1991)15983-5
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