Consider the class of closed Riemannian manifolds M of dimension dim (M) ≥ 3, Ricci curvature Ric(M) ≥ -(n - 1), diameter diam (M) < D and almost maximal volume. We show that the isomorphism types of fundamental groups characterize the diffeomorphism types of manifolds in such a class. In particular, it can be viewed as a generalization of the well-known Mostow's rigidity theorem and a finiteness theorem.
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