Skip to main content
Log in

Geometric applications of the solvability of Neumann problems on a Riemannian manifold

  • Published:
Archive for Rational Mechanics and Analysis 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.

Bibliography

  1. Aleksandrov, A. D., Uniqueness Theorems for Surfaces in the Large, V. American Math. Soc. Translations (2) 21 (1962), 412–416. MR27#698e.

    Google Scholar 

  2. Aleksandrov, A. D., A characteristic property of spheres. Ann. Mat. Pura Appl.(4) 58, 303–315 (1962), MR26 No. 722.

    Google Scholar 

  3. Berger, M., Gauduchon, P., & E. Mazet, Le spectre d'une variété Riemannienne. Springer Lecture Notes 194, (1971). MR 43 No. 8025.

  4. Bishop, R., & R. Crittenden, Geometry of manifolds. Pure and Applied Math., vol. XV. New York: Academic Press 1964. MR 29 No. 6401.

    Google Scholar 

  5. Bonnesen, T., & W. Fenchel, Konvexe Körper. New York: Chelsea Publishing Co., 1948.

    Google Scholar 

  6. Eisenhart, L. P., Riemannian Geometry. Princeton: University Press 1925.

    Google Scholar 

  7. Fiala, F., Le probléme des isopérimétres sur les surfaces ouvertes á courbure positive. Comm. Math. Helv. 13, 293–346 (1941), MR 3-301.

    Google Scholar 

  8. Gallot, S., Équations différentielles caractéristiques de la sphére. Ann. Sci. Ec. Norm. Super. Ser IV 12, 235–267 (1979).

    Google Scholar 

  9. Gray, A., The volume of a small geodesic ball of a Riemannian manifold. Michigan Math. J. 20, 329–344 (1973). MR 49 No. 3765.

    Google Scholar 

  10. Hörmander, L., Linear Partial Differential Operators. Berlin Heidelberg New York: Springer 1969. MR 40#1687.

    Google Scholar 

  11. Minkowski, H., Volumen und Oberfläche. Math. Ann. 57, 447–495 (1903).

    Google Scholar 

  12. Obata, M., Certain conditions for a Riemannian manifold to be isometric with a sphere. J. Math. Soc. Japan 14, 333–340 (1962), MR 25 No. 5479.

    Google Scholar 

  13. Reilly, R., Applications of the Hessian operator in a Riemannian manifold. Indiana Univ. Math. J. 26, 459–472 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by J. Serrin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reilly, R.C. Geometric applications of the solvability of Neumann problems on a Riemannian manifold. Arch. Rational Mech. Anal. 75, 23–29 (1980). https://doi.org/10.1007/BF00284618

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00284618

Keywords

Navigation