Skip to main content
SpringerLink
Log in

Curvature estimates for minimal hypersurfaces

  • Published:
Acta Mathematica

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. Almgren, F. J., Jr., Some interior regularity theorems for minimal surfaces and an extension of Bernstein's theorem.Ann. of Math., 84 (1966), 277–292.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bernstein, S., Sur un theoreme de geometrie et ses applications aux equations aux derivees partielles du type elliptique.Comm. de la Soc. Math. de Kharkov (2éme Ser.), 15 (1915–1917), 38–45.

    Google Scholar 

  3. Bombieri, E., De Giorgi, E. &Giusti, E., Minimal cones and the Bernstein problem.Invent. Math, 7 (1969), 243–268.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chern, S. S.,Minimal submanifolds in a Riemannian manifold. Mimeographed Lecture Notes, Univ. of Kansas, 1968.

  5. Chern, S. S., DoCarmo, M. &Kobayashi, S. Minimal submanifolds of a sphere with second fundamental form of constant length. InFunctional Analysis and Related Fields, edited by F. Browder, Springer-Verlag, Berlin, 1970.

    Google Scholar 

  6. De Giorgi, E., Una estensione del teorema di, Bernstein,Ann. Scuola Norm. Sup. Pisa, III, 19, (1965), 79–85.

    MathSciNet  Google Scholar 

  7. Fleming, W. H., On the oriented Plateau problem, Rend. Circ. Mat., Palermo, 2 (1962), 1–22.

    Google Scholar 

  8. Heinz, E., Über die Lösungen der Minimalflächengleichung,Nachr. Akad. Wiss. Göttingen Math., Phys. K1 II, (1952), 51–56.

    MathSciNet  Google Scholar 

  9. Hoffman, D. & Spruck, J, Sobolev inequalities on Riemannian manifolds. To appear inComm. Pure Appl. Math.

  10. Morrey, C. B.,Multiple integrals in the calculus of variations. New York, Springer-Verlag, 1966.

    MATH  Google Scholar 

  11. Osserman, R.,A survey of minimal surfaces. Van Nostrand Reinhold Math. Studies, 1969.

  12. Simons, J., Minimal varieties in Reimannian manifolds,Ann. of Math., 88 (1968), 62–105.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Stanford University, 94305, Stanford, CA, USA

    R. Schoen, L. Simon & S. T. Yau

Authors
  1. R. Schoen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Simon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. T. Yau
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the National Science Foundation Grant GP-35543, AFOSR Contract F-44620-72-C-0031 and Sloan Foundation Grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schoen, R., Simon, L. & Yau, S.T. Curvature estimates for minimal hypersurfaces. Acta Math. 134, 275–288 (1975). https://doi.org/10.1007/BF02392104

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392104

Keywords

Search

Navigation