Open manifolds with nonnegative Ricci curvature and large volume growth

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 $R^n$ .