Skip to main content
Log in

Curvature free volume estimates

  • Published:
Inventiones mathematicae Aims and scope

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. Berger, M.: Lectures on Geodesics in Riemannian Geometry. Tata Institute, Bombay, 1965

    Google Scholar 

  2. Berger, M.: Some relations between volume, injectivity radius, and convexity, radius in riemannian manifolds. In: Differential Geometry and Relativity (Cahen, Flato, Eds.). Dordrecht-Boston: D. Reidel 1976

    Google Scholar 

  3. Berger, M.: Une borne inférieure pour le volume d'une variété reimannienne en function du rayon d'injectivité. Ann. Inst. Fourier (Grenoble)30, 259–265 (1980)

    Google Scholar 

  4. Berger, M.: Volume et rayon d'injectivité dans les variétés riemanniennes, de dimension 3. Osaka J. Math.14, 191–200 (1977)

    Google Scholar 

  5. Berger, M., Kazdan, J.L.: A Sturm-Liouville inequality with applications to an isoperimetric inequality for volume in terms of injectivity radius, and to Wiedersehen manifolds, in General Inequalities 2 (Proceedings of the Second International Conference on General Inequalities, 1978), E.F. Beckenbach (ed.), ISNM47, 367–377. Basel: Birkhauser 1980

    Google Scholar 

  6. Besse, A.: Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik No. 93. Berlin Heidelberg New York: Springer 1978

    Google Scholar 

  7. Croke, C.: Some isoperimetric inequalities and Eigenvalue estimates. Ann. Sci. École Norm. Sup., 4e série13, 419–535 (1980)

    Google Scholar 

  8. Croke, C.: On the volume of metric balls. Proc. Amer. Math. Soc.88, 660–664 (1983)

    Google Scholar 

  9. Santaló, L.A.: Integral Geometry and Geometric Probability, (Encyclopedia of Mathematics and Its Applications). London-Amsterdam-Don Mills, Ontario-Sydney-Tokyo; Addison-Wesley 1976

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Research supported by NSF grant #MCS 79-01780 Max Planck Institute, and IHES

Rights and permissions

Reprints and permissions

About this article

Cite this article

Croke, C.B. Curvature free volume estimates. Invent Math 76, 515–521 (1984). https://doi.org/10.1007/BF01388471

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388471

Keywords

Navigation