Bishop's Inequality
Let 
be the volume of a Ball of radius 
in a complete 
-D Riemannian Manifold with RicciCurvature 
. Then 
, where 
is the volume of a Ball in a spacehaving constant Sectional Curvature. In addition, if equality holds for some Ball, then this Ballis 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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