Skip to main content
SpringerLink
Log in

On the existence of higher dimensional Enneper's surface

  • Published:
Commentarii Mathematici Helvetici

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

  • [A]M. Anderson,The compactification of a minimal submanifold in Euclidean space by the Gauss map, preprint.

  • [B]E. Bombieri,Recent progress in the theory of minimal surfaces, L'Enseignement Math.25 (1979), 1–8.

    MathSciNet  Google Scholar 

  • [BDG]E. Bombieri, E. DeGiorgi andE. Giusti,Minimal cones and the Bernstein problem, Invent. Math.7 (1969), 243–268.

    Article  MathSciNet  Google Scholar 

  • [C]J. Cheeger,A lower bound for the smallest eigenvalue of the Laplacian, “Problems in Analysis”, Princeton Univ. Press, Princeton, New Jersey, 1970, 195–199.

    Google Scholar 

  • [Ch]J. Choe,Index, vision number and stability of complete minimal surfaces, Arch. Rat. Mech. Anal.109 (1990), 195–212.

    Article  MathSciNet  Google Scholar 

  • [FK]D. Ferus andH. Karcher,Non-rotational minimal spheres and minimizing cones, Comment. Math. Helv.60 (1985), 247–269.

    MathSciNet  Google Scholar 

  • [F]D. Fischer-Colbrie,On complete minimal surfaces with finite Morse index in three manifolds, Invent. Math.82 (1985), 121–132.

    Article  MathSciNet  Google Scholar 

  • [GT]D. Gilbarg andN. S. Trudinger,Elliptic partial differential equations of second order, 2nd edn, Springer Verlag, Berlin, 1983.

    MATH  Google Scholar 

  • [JS]H. Jenkins andJ. Serrin,The Dirichlet problem for the minimal surface equation in higher dimensions, J. Reine Angew. Math.229 (1968), 170–187

    MathSciNet  Google Scholar 

  • [O]R. Osserman,Global properties of minimal surfaces in E 3 and E n, Ann. of Math.80 (1964), 340–364.

    Article  MathSciNet  Google Scholar 

  • [SS]R. Schoen andL. Simon,Regularity of stable minimal hypersurfaces, Comm. Pure Appl. Math.34 (1981), 741–797.

    MathSciNet  Google Scholar 

  • [SSY]R. Schoen, L. Simon andS.-T. Yau,Curvature estimates for minimal hypersurfaces, Acta Math.134 (1975), 275–288.

    Article  MathSciNet  Google Scholar 

  • [S]L. Simon,Remarks on curvature estimates for minimal hypersurfaces, Duke Math. J.43 (1976), 545–553.

    Article  MathSciNet  Google Scholar 

  • [Si]J. Simons,Minimal varieties in Riemannian manifolds, Ann. of Math.88 (1968), 62–105.

    Article  MathSciNet  Google Scholar 

  • [W]Q.-M. Wang,On a class of minimal hypersurfaces in R n, Math. Ann.298 (1994), 207–251.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Postech, 790-600, Pohang, South Korea

    Jaigyoung Choe

Authors
  1. Jaigyoung Choe
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by BSRI-94-1416, GARC, KOSEF (941-0100-016-2).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Choe, J. On the existence of higher dimensional Enneper's surface. Commentarii Mathematici Helvetici 71, 556–569 (1996). https://doi.org/10.1007/BF02566436

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02566436

Keywords

Search

Navigation