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.
- Circle Inscribing
- Circle Involute
- Circle Involute Pedal Curve
- Circle Lattice Points
- Circle Lattice Theorem
- Circle Map
- Circle Method
- Circle Negative Pedal Curve
- Circle Notation
- Circle Order
- Circle Orthotomic
- Circle Packing
- Circle Pedal Curve
- Circle-Point Midpoint Theorem
- Circle Radial Curve
- Circles-and-Squares Fractal
- Circle Squaring
- Circle Strophoid
- Circle Tangents
- Circuit
- Circuit Rank
- Circulant Determinant
- Circulant Graph
- Circulant Matrix
- Circular Cylindrical Coordinates