Cheeger's Finiteness Theorem
Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the number of diffeomorphisms classes of this set in terms of the constants n, d, V, and kappa.
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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 Resource. https://mathworld.wolfram.com/CheegersFinitenessTheorem.html