Skip to main content
SpringerLink
Log in

An unknotting result for complete minimal surfaces R3

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • [C,P] Carmo, M., do, Peng, C.K.: Stable minimal surfaces inR 3 are planes. Bulletin of the AMS, 1:903–906, 1979.

    Google Scholar 

  • [F-C] Fischer-Colbrie, D.: On complete minimal surfaces with finite Morse index in 3-manifolds. Invent. Math.82, 121–132 (1985)

    Google Scholar 

  • [F-C,S] Fischer-Colbrie, D., Schoen, R.: The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature. Comm. Pure Appl. Math.33, 199–211 (1980)

    Google Scholar 

  • [F,H,S] Freedman, M.H., Hass, J. and Scott, P.: Least area incompressible, surfaces in 3-manifolds. Invent. Math.71, 609–642 (1983)

    Google Scholar 

  • [F,M] Frohman, C., Meeks, W.H. III.: The topological uniqueness of complete one-ended minimal surfaces and Heegaard surfaces inR 3 (Preprint)

  • [H,M] Hoffman, D., Meeks, W.H. III.: The strong halfspace theorem for minimal surfaces. Invent Math. (to appear)

  • [L] Lawson, B.: The unknottedness of minimal embeddings. Invent. Math.11: 183–187, 1970

    Google Scholar 

  • [M,S,Y] Meeks, W.H. III., Simon, L., Yau, S.-T.: The existence of embedded minimal surface, exotic spheres and positive Ricci curvature. Ann. Math.116:221–250, 1982.

    Google Scholar 

  • [M,Y] Meeks, W.H. III., Yau, S.-T.: The topological uniqueness theorem of complete minimal surfaces of finite topological type. (Preprint)

  • [S1] Schoen, R.: Estimates for Stable Minimal Surfaces in Three Dimensional Manifolds, vol. 103 of Annals of Math. Studies. Princeton University Press, 1983.

  • [S2] Schoen, R.: Uniqueness, symmetry, and embeddedness, of minimal surfaces. J. Differ. Geom.18:791–809, 1983.

    Google Scholar 

  • [Si] Simon, L.: Lectures on geometric measure theory. In: Proc. of the Center for Mathematical Analysis, vol. 3, Australian National University, Canberra, Australia, 1983.

  • [St] Stallings, J.: On fibering certain 3-manifolds. In: Proc. The Univ. of Georgia Inst., 1961. Prentice Hall, 120–167 (1962).

  • [W] Waldhausen, F.: Heegaard-zerlegungen der 3-sphere. Topology7:195–203, 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, 92093-0112, La Jolla, CA, USA

    Michael H. Freedman

Authors
  1. Michael H. Freedman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Oblatum 1-V-1991

Partially supported by NSF grant DMS89-01412

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freedman, M.H. An unknotting result for complete minimal surfaces R3 . Invent Math 109, 41–46 (1992). https://doi.org/10.1007/BF01232017

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01232017

Keywords

Search

Navigation