Minimal surfaces bounded by a pair of convex planar curves

Authors:
William H. Meeks III and Brian White

Journal:
Bull. Amer. Math. Soc. **24** (1991), 179-184

MSC (1985):
Primary 53A10, 49F10; Secondary 58E12

DOI:
https://doi.org/10.1090/S0273-0979-1991-15983-5

MathSciNet review:
1069989

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References | Similar Articles | Additional Information

**1.**J. L. Barbosa and M. do Carmo,*On the size of a stable minimal surface in*R^{3}, Amer. J. Math. 19(8) (1976), 515-528. MR**413172****2.**M. Callahan, D. Hoffman, and W. H. Meeks III,*Embedded minimal surfaces with an infinite number of ends*, Invent. Math. 96 (1989), 459-505. MR**996552****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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DOI:
https://doi.org/10.1090/S0273-0979-1991-15983-5