Skip to main content
SpringerLink
Log in

On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space

  • 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

Bibliography

  1. Berger, M., Gauduchon, P. andMazet, E., Le spectre d'une variété Riemannienne, Lecture Notes in Math. #194, Springer-Verlag (1971) Berlin.

  2. Blaschke, W., Vorlesungen über Differentialgeometrie, I. Springer (1924) Berlin.

  3. Bleecker D. andWeiner, J., Extrinsic bounds on λ1 of Δ on a compact manifold, Comment. Math. Helv.51 (1976) 601–609.

    MATH  MathSciNet  Google Scholar 

  4. Hsiung, C. C., Some integral formulas for closed hypersurfaces, Math. Scand.,2 (1954) 286–294.

    MATH  MathSciNet  Google Scholar 

  5. Reilly, R. C., Applications of stereographic projections to submanifolds inEm andSm, Proc. AMS25 (1970) 119–123.

    Article  MATH  MathSciNet  Google Scholar 

  6. —, Variational properties of mean curvatures, Proc. 13th Biennial Seminar of the Canadian Math. Congress, vol II (1973) 102–114.

    Google Scholar 

  7. Takahashi, T., Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan18 (1966) 380–385.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, Warwickshire, England

    Robert C. Reilly

Authors
  1. Robert C. Reilly
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research for this paper was completed while the author was on sabbatical leave from the University of California (Irvine) and in residence at the Mathematics Institute of the University of Warwick.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reilly, R.C. On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space. Commentarii Mathematici Helvetici 52, 525–533 (1977). https://doi.org/10.1007/BF02567385

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567385

Keywords

Search

Navigation