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The topology of complete one-ended minimal surfaces and Heegaard surfaces in ${\text{R}}^3$
Author(s):
Charles
Frohman;
William H.
Meeks III
Journal:
Bull. Amer. Math. Soc.
23
(1990),
417-421.
MSC (1985):
Primary 53A10, 57M99
MathSciNet review:
1033085
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Additional information
References:
- [1] M. Callahan, D. Hoffman, and W. H. Meeks III, The structure of singlyperiodic minimal surfaces, Invent. Math. 99 (1990), 455-481. MR 1032877
- [2] T. Frankel, On the fundamental group of a compact minimal submanifold, Ann. of Math. 83 (1966), 68-73. MR 187183
- [3] M. Freedman, J. Hass, and P. Scott, Least area incompressible surfaces in 3-manifolds, Invent. Math. 71 (1983), 609-642. MR 695910
- [4] C. Frohman, The topological uniqueness of triply-periodic minimal surface in R3, J. Differential Geom. 31 (1990), 277-283. MR 1030674
- [5] C. Frohman and W. H. Meeks III, The ordering theorem for the ends of properly embedded minimal surfaces, preprint.
- [6] C. Frohman and W. H. Meeks III, The topological uniqueness of complete one-ended minimal surfaces and Heegaard surfaces in R3, preprint.
- [7] W. Haken, Some results on surfaces in 3-manifolds, Studies in Modern Topology, 1968. MR 224071
- [8] D. Hoffman and W. H. Meeks III, The strong halfspace theorem for minimal surfaces, Invent. Math. 5, 39-98.
- [9] H. B. Lawson, The unknottedness of minimal embeddings, Invent. Math. 11 (1970), 183-187. MR 287447
- [10] W. H. Meeks III, The topological uniqueness of minimal surfaces in three-dimensional Euclidean space, Topology 20 (1981), 389-410. MR 617373
- [11] W. H. Meeks III, L. Simon, and S. T. Yau, The existence of embedded minimal surfaces, exotic spheres and positive Ricci curvature, Ann. of Math. 116 (1982), 221-259.
- [12] W. H. Meeks III and S. T. Yau, The topological uniqueness theorem of complete minimal surfaces of finite topological type, preprint.
- [13] R. Schoen, Estimates for stable minimal surfaces in three dimensional manifolds, Ann. of Math. Stud., vol. 103, Princeton Univ. Press, Princeton, N.J., 1983, 111-126. MR 795231
- [14] F. Waldhausen, Heegaard zerlegungen von der drie-sphaere, Topology 7 (1968), 195-203. MR 227992
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Additional Information:
DOI:
10.1090/S0273-0979-1990-15947-6
PII:
S 0273-0979(1990)15947-6
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