Embedded minimal surfaces: Forces, topology and symmetries

Calculus of Variations and Partial Differential Equations

Volumn 4, Issue 5, 1996, Pages 469-496

  Ros, Antonio ^a  

^a UNIVERSITY OF GRANADA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0013489708     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01246152     Document Type: Article

References (22)

1. α-compactness for manifolds with Ricci curvature and injectivity radius bounded below. J. Diff. Geom. 35, 265-281 (1992)
2. Cheeger, J.: Finiteness theorems for Riemannian manifolds. Amer. J. Math. 92, 64-71 (1970)
3. 3 of genus one and three embedded ends. Bull. Soc. Bras. Math. 15, 47-54 (1984)
4. Hoffman, D., Meeks, W.H., III.: The strong halfspace theorem for minimal surfaces. Invent. Math. 101, 373-377 (1990)
5. Hoffman, D., Meeks, W.H., III.: Embedded minimal surfaces of finite topology. Ann. Math. 131, 1-34 (1990)
6. Kasue, A.: A convergence theorem for Riemannian manifolds and some applications. Nagoya Math. J. 114, 21-51 (1989)
7. Korevaar, N., Kusner, R.: The structure of constant mean curvature embeddings in Euclidean three-space. In: Greene, R., Yau, S.T. (eds.) Proc. Symp. Pure Math. 54 part 1, 291-297 (1993)
8. Langevin, R., Rosenberg, H.: A maximum principle at infinity for minimal surfaces and applications. Duke Math. J. 57, 819-828 (1988)
9. Lopez, F., Ros, A.: On embedded complete minimal surfaces of genus zero. J. Diff. Geom. 33, 293-300 (1991)
10. Meeks, W.H., III.: The topological uniqueness minimal surfaces in three-dimensional Euclidean space. Topology 20, 389-410 (1981)
11. Meeks, W.H., III., Rosenberg, H.: The maximum principle at infinity for minimal surfaces in flat three manifolds. Comment. Math. Helv. 65, 255-270 (1990)
12. Meeks, W.H., III., White, B.: Minimal surfaces bounded by a pair of convex planar curves. Bull. A.M.S. 24, 179-184 (1991)
13. Meeks, W.H., III., White, B.: Minimal surfaces bounded by convex curves in parallel planes. Comment. Math. Helv. 66, 263-278 (1991)
14. Meeks, W.H., III., Yau, S.T.: The existence of embedded minimal surfaces and the problem of uniqueness. Math. Zeit. 179, 151-168 (1982)
15. Meeks, W.H., III., Yau, S.T.: The topological uniqueness of complete minimal surfaces of finite topological type. Topology 31, 305-316 (1992)
16. Osserman, R.: A survey of minimal surfaces. Dover Publications, New York, 2nd edn, 1986
17. Perez, J., Ros, A.: Some uniqueness and nonexistence theorems for embedded minimal surfaces. Math. Ann. 295, 513-525 (1993)
18. Ritore, M., Ros, A.: The spaces of index one minimal surfaces and stable constant mean curvature surfaces embedded in flat three manifolds. Trans. of Amer. Math. Soc. 348, 391-410 (1996)
19. Ros, A.: The Gauss map of minimal surfaces. Preprint
20. Schoen, R.: Uniqueness, symmetry and embeddedness of minimal surfaces. J. Diff. Geom. 18, 791-809 (1983)
21. Schoen, R.: Estimates for stable minimal surfaces in three dimensional manifolds. Volume 103 of Annals of Math. Studies. Princeton University Press, 1983
22. Shiffman, M.: On surfaces of stationary area bounded by two circles, or convex curves, in parallel planes. Ann. of Math. 63, 77-99 (1956)