Let be the volume of a Ball of radius in a complete -D Riemannian Manifold with Ricci Curvature . Then , where is the volume of a Ball in a space having constant Sectional Curvature. In addition, if equality holds for some Ball, then this Ball is Isometric to the Ball of radius in the space of constant Sectional Curvature .

**References**

Chavel, I. *Riemannian Geometry: A Modern Introduction.* New York: Cambridge University Press, 1994.

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1999-05-26