Skip to main content
SpringerLink
Log in

A maximum principle at infinity and the topology of complete embedded surfaces with constant mean curvature

  • Conference paper
  • First Online:
Global Differential Geometry and Global Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1481))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. L. Caffarelli, R. Hardt, and L. Simon. Minimal surfaces with isolated singularities. Manuscripta Math., 48:1–18, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. Earp and H. Rosenberg. Some remarks on surfaces of prescribed mean curvature. preprint.

    Google Scholar 

  3. T. Frankel. On the fundamental group of a compact minimal submanifold. Annals of Math., 83:68–73, 1966.

    Article  MathSciNet  MATH  Google Scholar 

  4. N. Kapouleas. Complete constant mean curvature surfaces in Euclidean three space. Annals of Math., 131:239–330, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  5. N. Korevaar and R. Kusner. The global structure of constant mean curvature surfaces. in preparation.

    Google Scholar 

  6. N. Korevaar, R. Kusner, and B. Solomon. The structure of complete embedded surfaces with constant mean curvature. Journal of Differential Geometry, 30:465–503, 1989.

    MathSciNet  MATH  Google Scholar 

  7. R. Kusner. Compactness for families of constant mean curvature surfaces. in preparation.

    Google Scholar 

  8. R. Kusner. Bubbles, conservation laws and balanced diagrams. In P. Concus, R. Finn, and D. Hoffman, editors, Geometric Analysis and Computer Graphics, volume 17 of MSRI Publications. Springer-Verlag, 1990.

    Google Scholar 

  9. R. Langevin and H. Rosenberg. A maximum principle at infinity for minimal surfaces and applications. Duke Math. Journal, 57:819–828, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  10. H. B. Lawson. The unknottedness of minimal embeddings. Inventiones Math., 11:183–187, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  11. W. H. Meeks III and S. T. Yau. The topological uniqueness of complete minimal surfaces of finite topological type. to appear in Topology.

    Google Scholar 

  12. W. H. Meeks III and S. T. Yau. Topology of three-manifolds and the embedding problems in minimal surface theory. Annals of Math., 112:441–484, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  13. R. Schoen and S. T. Yau. Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature. Annals of Math., 110:127–142, 1979.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Rob Kusner

Authors
  1. Rob Kusner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Dirk Ferus Ulrich Pinkall Udo Simon Berd Wegner

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Kusner, R. (1991). A maximum principle at infinity and the topology of complete embedded surfaces with constant mean curvature. In: Ferus, D., Pinkall, U., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 1481. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0083634

Download citation

  • DOI: https://doi.org/10.1007/BFb0083634

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54728-0

  • Online ISBN: 978-3-540-46445-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation