Consider the set of compact 
-Riemannian manifolds 
with diameter
,
Volume
,
and 
where 
is the sectional curvature. Then there is
a bound on the number of diffeomorphisms classes
of this set in terms of the constants 
, 
, 
, and 
.
Cheeger's Finiteness Theorem
Explore with Wolfram|Alpha
References
Chavel, I. Riemannian Geometry: A Modern Introduction. New York: Cambridge University Press, 1994.Referenced on Wolfram|Alpha
Cheeger's Finiteness TheoremCite this as:
Weisstein, Eric W. "Cheeger's Finiteness Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CheegersFinitenessTheorem.html