Mathematische Zeitschrift

, Volume 197, Issue 1, pp 123–138 | Cite as

Stability of hypersurfaces of constant mean curvature in Riemannian manifolds

  • J. Lucas Barbosa
  • Manfredo do Carmo
  • Jost Eschenburg
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References

  1. [A]
    Abresch, U.: Constant mean curvature tori in terms of elliptic functions, Preprint MPI-SFB 85-50, Bonn, 1985Google Scholar
  2. [BdC]
    Barbosa, J.L., do Carmo, M.: Stabilty of hypersurfaces with constant mean curvature. Math. Z.185, 339–353 (1984)Google Scholar
  3. [BGM]
    Berger, M., Gauduchon, P., Mazet, E.: Le spectre d'une variété Riemanniene, Lect. Notes Math.194. Berlin-Heidelberg-New York: Springer 1971Google Scholar
  4. [H]
    Heintze, E.: Extrinsic upper bounds for λ1. Preprint Univ. Augsburg No. 93, 1986Google Scholar
  5. [HTY]
    Hsiang, W.Y., Teng, Z.H., Yu, W.: New examples of constant mean curvature immersions of (2k−1)-spheres into Euclidean 2k-space. Ann. Math.117, 609–625 (1983)Google Scholar
  6. [L]
    Lawson, H.B., Jr.: Lectures on minimal submanifolds, vol. I. Math. Lecture Series, 9. Boston: Publish or Perish 1980Google Scholar
  7. [O'N]
    O'Neill, B.: The fundamental equations of a submersion. Mich. Math. J.,23, 459–469 (1966)Google Scholar
  8. [S]
    Silveira, A.M. da: Stable complete surfaces with constant mean curvature. Math. Ann.277, 629–638 (1987)Google Scholar
  9. [Sc]
    Schmidt, E.: Beweis der isoperimetrischen Eigenschaft der Kugel im hyperbolischen und sphärischen Raum jeder Dimensionszahl. Math. Z.49, (1943/44)Google Scholar
  10. [W]
    Wente, H.: Counter-example to the Hopf conjecture. Pac. J. Math.121, 193–244 (1986)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. Lucas Barbosa
    • 1
  • Manfredo do Carmo
    • 2
  • Jost Eschenburg
    • 3
  1. 1.Departamento de MatemáticaUniversidade Federal do CearáFortalezaBrasil
  2. 2.Instituto de Matemática Pura e AplicadaRio de JaneiroBrasil
  3. 3.Mathematisches Institut der UniversitätFreiburgFederal Republic of Germany

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