## Bishop's Inequality

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.