Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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
DOI: https://doi.org/10.1090/S0273-0979-1990-15947-6
MathSciNet review: 1033085
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 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, https://doi.org/10.1007/BF01234428
  • [2] T. Frankel, On the fundamental group of a compact minimal submanifold, Ann. of Math. 83 (1966), 68-73. MR 187183
  • Michael Freedman, Joel Hass, and Peter Scott, Least area incompressible surfaces in 3-manifolds, Invent. Math. 71 (1983), no. 3, 609–642. MR 695910, https://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
  • [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
  • William H. Meeks III, The topological uniqueness of minimal surfaces in three-dimensional Euclidean space, Topology 20 (1981), no. 4, 389–410. MR 617373, https://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
  • [14] F. Waldhausen, Heegaard zerlegungen von der drie-sphaere, Topology 7 (1968), 195-203. MR 227992

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 53A10, 57M99

Retrieve articles in all journals with MSC (1985): 53A10, 57M99


Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1990-15947-6

American Mathematical Society