Skip to main content
Log in

Stability of hypersurfaces with constant mean curvature

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Barbosa, J.L., do Carmo, M.: Stability of minimal surfaces and eigenvalues of the Laplacian. Math. Z.173, 13–28 (1980)

    Google Scholar 

  2. Böhme, R., Tomi, F.: Zur Struktur der Lösungsmenge des Plateauproblems. Math. Z.133, 1–29 (1973)

    Google Scholar 

  3. Bolza, O.: Vorlesungen über Variationsrechnung. Berlin-Leipzig: Teubner 1909

    Google Scholar 

  4. do Carmo, M., Peng, C.K.: Stable complete minimal surfaces inR 3 are planes. Bull. Amer. Math. Soc. (N.S.),1, 903–906 (1979)

    Google Scholar 

  5. Fischer-Colbrie, D., Schoen, R.: The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature. Comm. Pure Appl. Math.35, 199–211 (1980)

    Google Scholar 

  6. Frid, H.: O Teorema do índice de Morse. Master's thesis, IMPA 1982

  7. Frid, H., Thayer, F.J.: The Morse index theorem for elliptic problems with a constraint. An. Acad. Brasil. Ci.55, 9–10 (1983)

    Google Scholar 

  8. Hsiang, W.Y., Teng, Z.H., Yu, W.: New examples of constant mean curvature immersions of (2k-1)-spheres into euclidean 2k-space. Ann. of Math.117, 609–625 (1983)

    Google Scholar 

  9. Kenmotsu, K.: Surfaces of revolution with prescribed mean curvature. Tôhoku Math. J.32, 147–153 (1980)

    Google Scholar 

  10. Lawson, B., Jr.: Lectures on Minimal Submanifolds, vol.1. Berkeley: Publish or Perish 1980

    Google Scholar 

  11. Mori, H.: Stable constant mean curvature surfaces inR 3 and inH 3. Preprint

  12. Pogorelov, A.V.: On the stability of minimal surfaces. Soviet. Math. Dokl.24, 274–276 (1981)

    Google Scholar 

  13. Ruchert, H.: Ein Eindeutigkeitssatz für Flächen konstanter mittlerer Krümmung. Arch. Math. (Basel)33, 91–104 (1979)

    Google Scholar 

  14. D'Arcy Thompson: On growth and form. New York: Cambridge at the University Press and The MacMillan Co 1945

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barbosa, J.L., do Carmo, M. Stability of hypersurfaces with constant mean curvature. Math Z 185, 339–353 (1984). https://doi.org/10.1007/BF01215045

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01215045

Navigation