Finiteness theorem

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This article describes a result related to the sectional curvature of a Riemannian manifold


Let n \in \mathbb{N}, \Lambda < \infty, D < \inftym and v > 0. Then consider the space S of differential manifolds M admitting a metric g for which:

dim(M) = n, |K| \le \Lambda, diam(M) \le D, vol(M) \ge v

where K denotes the sectional curvature.

Then, S consists of finitely many diffeomorphism classes/types.