Let 
be a compact 
-dimensional manifold with injectivity radius 
. Then
 |
with equality iff 
is isometric to the standard
round sphere 
with radius 
, where 
is the volume of the standard
-hypersphere of radius 
.
Berger-Kazdan Comparison Theorem
See also
Blaschke Conjecture, Hypersphere, Injection, IsometryExplore with Wolfram|Alpha
References
Chavel, I. Riemannian Geometry: A Modern Introduction. New York: Cambridge University Press, 1994.Referenced on Wolfram|Alpha
Berger-Kazdan Comparison TheoremCite this as:
Weisstein, Eric W. "Berger-Kazdan Comparison Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Berger-KazdanComparisonTheorem.html