Abstract

In this paper, we study complete open n-dimensional Riemannian manifolds with nonnegative Ricci curvature and large volume growth. We prove among other things that such a manifold is diffeomorphic to a Euclidean n-space \( R^n \) if its sectional curvature is bounded from below and the volume growth of geodesic balls around some point is not too far from that of the balls in \( R^n \).

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