Skip to main content
SpringerLink
Log in

Maximum principles for minimal surfaces in ℝ3 having noncompact boundary and a uniqueness theorem for the helicoidhaving noncompact boundary and a uniqueness theorem for the helicoid

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

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. P. Collin, R. Krust:Le problème de Dirichlet pour l’équation des surfaces minimales sur de domaines non bornés, Bull. Soc. Math. de France 119, 443–462, 1991

    MATH  MathSciNet  Google Scholar 

  2. U. Dierkes:Maximum principles and nonexistence results for minimal submanifolds, Manuscripta Math. 69, 203–218, 1990

    MATH  MathSciNet  Google Scholar 

  3. D. Gilbarg, N. S. Trudinger:Elliptic Partial Differential Equations of Second Order, 2 nd edition, Springer-Verlag, 1983

  4. S. Hildebrandt:Maximum Principles for minimal surfaces and for surfaces with continuous mean curvature, Math. Z. 128, 253–269, 1972

    Article  MATH  MathSciNet  Google Scholar 

  5. P. Hartman, A. Wintner:On the local behaviour of solutions of non-parabolic partial differential equations, American Journal of Mathematics, 75 (1953), 449–476

    Article  MATH  MathSciNet  Google Scholar 

  6. W. Meeks III, H. Rosenberg:The maximum principle at infinity for minimal surfaces in flat three manifoleds, Comentari Mathematici Helvetici 65, 255–270, 1990

    Article  MATH  MathSciNet  Google Scholar 

  7. R. Osserman:A survey of minimal surfaces, Van Nostrand-Reinhold, New York, 1969

    MATH  Google Scholar 

  8. J. C. C. Nitsche:Vorlesungen über Minimalflächen, Springer Verlag, 1975

  9. H. Rosenberg, E. Toubiana:Some remarks on deformations of minimal surfaces, Transactions of the AMS, Vol 295, N.2, 491–499, 1986

    Article  MATH  MathSciNet  Google Scholar 

  10. R.Schoen:Estimates for stable minimal surfaces in three-dimensional manifolds, Vol 103, Annals of Math. Studies, Princeton University Press, 1983

  11. M. Soret:Déformations de surfaces minimales, Thèse, Université Paris VII, 1993

  12. W. Ziemer:Weakly differentiable functions. Sobolev spaces and functions of bounded variation, Graduate Texts in Mathematics, Vol 120, Springer-Verlag, 1989

Download references

Author information

Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal do R. G. do Sul, Av. Bento Gonçalves 9500, 91509-900, Porto Algegre, RS, Brazil

    Jaime Ripoll

  2. Mathematisches Institut, Universität Heidelberg, In Neuenheimer Feld 288, D-69120, Heidelberg, Germany

    Friedrich Tomi

Authors
  1. Jaime Ripoll
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Friedrich Tomi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ripoll, J., Tomi, F. Maximum principles for minimal surfaces in ℝ3 having noncompact boundary and a uniqueness theorem for the helicoidhaving noncompact boundary and a uniqueness theorem for the helicoid. Manuscripta Math 87, 417–434 (1995). https://doi.org/10.1007/BF02570484

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02570484

Keywords

Search

Navigation