The topology of complete one-ended minimal surfaces and Heegaard surfaces in 𝑅³

Frohman, Charles; Meeks, William H., III

doi:10.1090/S0273-0979-1990-15947-6

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-9485(online) ISSN 0273-0979(print)

The topology of complete one-ended minimal surfaces and Heegaard surfaces in ${\text{R}}^3$

Authors: Charles Frohman and William H. Meeks III
Journal: Bull. Amer. Math. Soc. 23 (1990), 417-421
MSC (1985): Primary 53A10, 57M99
MathSciNet review: 1033085
Full-text PDF

Michael Callahan, David Hoffman, and William H. Meeks III, The structure of singly-periodic minimal surfaces, Invent. Math. 99 (1990), no. 3, 455–481. MR 1032877 (92a:53005), http://dx.doi.org/10.1007/BF01234428
T. Frankel, On the fundamental group of a compact minimal submanifold, Ann. of Math. (2) 83 (1966), 68–73. MR 0187183 (32 #4637)
Michael Freedman, Joel Hass, and Peter Scott, Least area incompressible surfaces in 3-manifolds, Invent. Math. 71 (1983), no. 3, 609–642. MR 695910 (85e:57012), http://dx.doi.org/10.1007/BF02095997
Charles Frohman, The topological uniqueness of triply periodic minimal surfaces in 𝑅³, J. Differential Geom. 31 (1990), no. 1, 277–283. MR 1030674 (92e:53008)
[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.
Wolfgang Haken, Some results on surfaces in 3-manifolds, Studies in Modern Topology, Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.), 1968, pp. 39–98. MR 0224071 (36 #7118)
[8] D. Hoffman and W. H. Meeks III, The strong halfspace theorem for minimal surfaces, Invent. Math. 5, 39-98.
H. Blaine Lawson Jr., The unknottedness of minimal embeddings, Invent. Math. 11 (1970), 183–187. MR 0287447 (44 #4651)
William H. Meeks III, The topological uniqueness of minimal surfaces in three-dimensional Euclidean space, Topology 20 (1981), no. 4, 389–410. MR 617373 (82h:53010), http://dx.doi.org/10.1016/0040-9383(81)90021-5
[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.
Richard Schoen, Estimates for stable minimal surfaces in three-dimensional manifolds, Seminar on minimal submanifolds, Ann. of Math. Stud., vol. 103, Princeton Univ. Press, Princeton, NJ, 1983, pp. 111–126. MR 795231 (86j:53094)
Friedhelm Waldhausen, Heegaard-Zerlegungen der 3-Sphäre, Topology 7 (1968), 195–203 (German). MR 0227992 (37 #3576)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|