Kodai Mathematical Journal

An estimate on the volume of metric balls

Shigeru Kodani

Full-text: Open access

Article information

Source
Kodai Math. J. Volume 11, Number 2 (1988), 300-305.

Dates
First available in Project Euclid: 23 January 2006

Permanent link to this document
http://projecteuclid.org/euclid.kmj/1138038881

Mathematical Reviews number (MathSciNet)
MR0949136

Zentralblatt MATH identifier
0667.53035

Digital Object Identifier
doi:10.2996/kmj/1138038881

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 53C65: Integral geometry [See also 52A22, 60D05]; differential forms, currents, etc. [See mainly 58Axx]

Citation

Kodani, Shigeru. An estimate on the volume of metric balls. Kodai Mathematical Journal 11 (1988), no. 2, 300--305. doi:10.2996/kmj/1138038881. http://projecteuclid.org/euclid.kmj/1138038881.


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References

  • [1] M. BERGER, Some relations between volume, injectivity radius, and convexity radius in Riemannian manifolds. Differential Geometry and relativity (Cahen, Flato, Eds.), D. Reidel, Dordrecht-Boston, 1976.
  • [2] M. BERGER, Volume et rayon d'injectivite dans les varietes riemanniennes d dimension 3, Osaka J. Math. 14(1977), 191-200.
  • [3] M. BERGER AND J. L. KAZDAN, A Sturm-Liouville inequality with applications t anisoperimetric inequality for volume in terms of injectivity radius, and to Wiedersehen manifolds, in General inequalities 2 (Proceedings of Second Inter-national Conference on General Inequalities, 1978), E. F. Beckenbach (ed.), ISNM47, 367-377, Basel, Birkhauser 1980.
  • [4] C. B. CROKE, Some isoperimetric inequalities and Eigenvalue estimates, Ann. Sci Ecole Norm. Sup. (4) 13 (1980), 419-535.
  • [5] C. B. CROKE, On the volume of metric balls, Proc. Amer. Math. Soc. 88 (1983), 660-664
  • [6] C. B. CROKE, Curvature free volume estimates, Invent, math. 76 (1984), 515-521
  • [7] J. CHEEGER AND D. EBIN, Comparison Theorems in Riemannian Geometry, Nort Holland, Amsterdam, Oxford, (1975).
  • [8] R. BISHOP AND R. CRITTENDEN, Geometryofmanifolds, Academic Press, New York, 1964