Skip to main content
SpringerLink
Log in

Embedding and surrounding with positive mean curvature

  • 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

  • [CG] Cheeger, J., Gromoll, D.: On the structure of complete open manifolds of non-negative curvature. Ann. Math.96, 413–443 (1972)

    Google Scholar 

  • [F1] Federer, H.: Geometric Measure Theory. New York: Springer 1969

    Google Scholar 

  • [F2] Federer, H.: The singular sets ofarea minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension. Bull. A.M.S.76, 767–771 (1970)

    Google Scholar 

  • [G] Gromov, M.: Stable mappings of foliations into manifolds. Izv. Akad. Nauk. S.S.S.R. Ser. Mat.33, 707–734 (1969); Math U.S.S.R. Izv.3, 671–694 (1969)

    Google Scholar 

  • [GL] Gromov, M., Lawson, H.B., Jr.: Spin and scalar curvature in the presence of a fundamental group, I. Ann. Math.111, 209–230 (1980)

    Google Scholar 

  • [HS] Hardt, R., Simon, L.: Boundary regularity and embedded solutions for the oriented Plateau Problem. Ann. Math.110, (1979)

  • [Hi] Hirsch, M.: Immersions of manifolds. Trans. Am. Math. Soc.93, 242–276 (1959)

    Google Scholar 

  • [L1] Lawson, H.B., Jr.: The unknottedness of minimal embeddings. Invent. Math.11, 183–187 (1970)

    Google Scholar 

  • [L2] Lawson, H.B., Jr.: Lectures on minimal submanifolds. Berkeley: Publish or Perish (1973)

    Google Scholar 

  • [LM] Lawson, H.B., Jr., Michelsohn, M.-L.: Approximation by positive mean curvature immersions: frizzing. Invent. Math.77, 421–426 (1984)

    Google Scholar 

  • [MSY] Meeks, W., III, Simon, L., Yau, S.T.: Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. Ann. Math.116, 621–659 (1982)

    Google Scholar 

  • [MY] Meeks, W., III, Yau, S.T.: The existence of embedded minimal surfaces and the problem of uniqueness. Math. Z.179, 151–168 (n o 2) (1982)

    Google Scholar 

  • [Mi] Milnor, J.: Lectures on theh-cobordism theorem. Princeton Mathematical No≧w Princeton N. J.: Princeton. Univ. Press (1965)

    Google Scholar 

  • [Ph] Phillips, A.: Submersions of open manifolds. Topology6, 171–206 (1967)

    Google Scholar 

  • [Po] Poenaru, V.: Sur la théorie des immersions. Topology1, 81–100 (1962)

    Google Scholar 

  • [Se] Serrin, J.: The Dirichlet problem for the minimal surface equation in higher dimensions. J. Reine Angew. Math.223, 170–187 (1968)

    Google Scholar 

  • [Sh] Sha, J.: Thesis, S.U.N.Y. Stony Brook 1984

  • [Sm] Smale, S.: The classification of immersions of spheres in Euclidean spaces. Ann. Math.69, 327–344 (1959)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, S.U.N.Y. at Stony Brook, 11794, Stony Brook, NY, USA

    H. Blaine Lawson Jr.

  2. Laboratoire associé au C.N.R.S. n° 169, Centre de Mathématiques de l'Ecole Polytechnique, Plateau de Palaiseau, F-91128, Palaiseau Cedex, France

    H. Blaine Lawson Jr.

  3. Department of Mathematics, S.U.N.Y. at Stony Brook, 11794, Stony Brook, NY, USA

    Marie-Louise Michelsohn

  4. I.H.E.S., 35, route de Chartres, F-91440, Bures sur Yvette, France

    Marie-Louise Michelsohn

Authors
  1. H. Blaine Lawson Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marie-Louise Michelsohn
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research partially supported by N.S.F. Grant No. MCS 830 1365 and the Guggenheim Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lawson, H.B., Michelsohn, ML. Embedding and surrounding with positive mean curvature. Invent Math 77, 399–419 (1984). https://doi.org/10.1007/BF01388830

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388830

Search

Navigation