Skip to main content

On complete minimal surfaces with parallel and flat ends

Part of the Lecture Notes in Mathematics book series (2803,volume 1369)

Abstract

In this paper we have proved the non-existence of minimal surfaces with 5 flat ends and presented some new examples of minimal surfaces with parallel and flat ends.

Keywords

  • Riemann Surface
  • Minimal Surface
  • Meromorphic Function
  • Linear Fractional Transformation
  • Minimal Immersion

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.95
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Peng C.K. Some new examples of minimal surfaces in R 3 and its applications, MSRI 07510-85.

    Google Scholar 

  2. L.P. Jorge and W.H. Meeks The topology of complete minimal surfaces of finite total Gaussian curvature. Topology, 22(1983) 203–221.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. R. Osserman Assurvey of minimal surfaces, Van Nostrand Reinhold, New York, (1969).

    Google Scholar 

  4. Xiao L. Some Results on pseudo-embedded minimal surfaces in R 3. To appear in Acta Mathematica Sinica.

    Google Scholar 

  5. R. Schoen Uniqueness, symmetry, and embeddedness of minimal surfaces, J.Differential Geometry, 18(1983), 791–809.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1989 Springer-Verlag

About this paper

Cite this paper

Xiao, L. (1989). On complete minimal surfaces with parallel and flat ends. In: Jiang, B., Peng, CK., Hou, Z. (eds) Differential Geometry and Topology. Lecture Notes in Mathematics, vol 1369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087542

Download citation

  • DOI: https://doi.org/10.1007/BFb0087542

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51037-6

  • Online ISBN: 978-3-540-46137-1

  • eBook Packages: Springer Book Archive