Skip to main content
SpringerLink
Log in

The geometry and conformal structure of properly embedded minimal surfaces of finite topology in 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

  1. Callahan, M., Hoffman, D., Meeks, W.H., III: The structure of singly-periodic manimal surfaces. Invent. Math.99, 455–481 (1990)

    Google Scholar 

  2. Collin, P., Krust, R.: Le probleme de Dirichlet pour l'equation des surfaces minimales sur des domaines non bornes. Bull. Soc. Math. Fr.120, 101–120 (1991)

    Google Scholar 

  3. Costa, C.: Example of a complete minimal immersion in ℝ3 of genus one and three embedded ends. Bull. Soc. Bras. Mat.15, 47–54 (1984)

    Google Scholar 

  4. Costa, C.: Uniqueness of minimal surfaces embedded in ℝ3 with total curvature 12π. J. Differ. Geom.30 (3), 597–618 (1989)

    Google Scholar 

  5. Fang, Y., Meeks, W.H., III: Some global properties of complete minimal surfaces of finite topology in ℝ3. Topology30 (1), 9–20 (1991)

    Google Scholar 

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

    Google Scholar 

  7. Frohman, C., Meeks, W.H., III: The ordering theorem for the ends of properly embedded minimal surfaces. (Preprint)

  8. Hoffman, D.: The discovery of new embedded minimal surfaces: Elliptic functions, symmetry; computer graphics. In: Proceedings of the Berlin Conference on Global Differential Geometry. (Springer Lect. Ser., vol. 1748) Berlin Heidelberg New York: Springer 1985

    Google Scholar 

  9. Hoffman, D., Karcher, H., Wei, F.: The genus-one helicoid, and the surfaces that led to its discovery. Bull AMS29, 77–84 (1993)

    Google Scholar 

  10. Hoffman, D., Meeks, W.H., III: The asymptotic behavior of properly embedded minimal surfaces of finite topology. J Am. Math. Soc.2 (4), 667–681 (1989)

    Google Scholar 

  11. Hoffman, D., Meeks, W.H., III: Embedded minimal surfaces of finite topology. Ann. Math.131, 1–34 (1990)

    Google Scholar 

  12. Hoffman, D., Meeks, W.H., III: The strong halfspace theorem for minimal surfaces. Invent. Math.101, 373–377 (1990)

    Google Scholar 

  13. Lopez, F.J., Ros, A.: On embedded complete minimal surfaces of genus zero. J. Diff. Geom.33 (1), 293–300 (1991)

    Google Scholar 

  14. Meeks, W.H., III, Rosenberg, H.: The maximum principle at infinity for minimal surfaces in flat three-manifolds. Comment. Math. Helv.65, 255–270 (1990)

    Google Scholar 

  15. Meeks, W.H., III, Yau, S.T.: The equivariant Dehn's lemma and loop theorem. Comment. Math. Helv.56, 225–239 (1981)

    Google Scholar 

  16. Rosenberg, H., Toubiana, E.: A cylindrical type complete minimal surface in a slab of R3. Bull. Sci. Math., III. Ser. 241–245 (1987)

  17. Schoen, R.: Estimates for Stable Minimal Surfaces in Three Dimensional Manifolds. (Ann. Math. Stud., Vol. 103) Princeton: Princeton University Press 1983

    Google Scholar 

  18. Schoen, R.: Uniqueness, symmetry, and embeddedness of minimal surfaces. J. Diff. Geom.18, 791–809 (1983)

    Google Scholar 

  19. Simon, L.: Lectures on geometric measure theory. In: Proceedings of the Center for Mathematical Analysis, vol. 3. Canberra, Australia, 1983. Australian National University 1984

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Massachusetts, 01003, Amherst, MA, USA

    William H. Meeks III

  2. Departement de Mathematiques, Université Paris VII, 2, Place Jussieu, F-75251, Paris Cedex 05, France

    Harold Rosenberg

Authors
  1. William H. Meeks III
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harold Rosenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Oblatum 7-VII-1992 & 13-IV-1993

The research described in this paper was supported by research grant DE-FG 02-86ER250125 of the Applied Mathematical Science subprogram of Office of Energy Research, US Department of Energy, and National Science Foundation grant DMS-9204535

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meeks, W.H., Rosenberg, H. The geometry and conformal structure of properly embedded minimal surfaces of finite topology in ℝ3 . Invent Math 114, 625–639 (1993). https://doi.org/10.1007/BF01232681

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01232681

Keywords

Search

Navigation