Complete manifolds with sectional curvature bounded below and large volume growth

This paper provides a proof that an n-dimensional complete open Riemannian manifold M with sectional curvature K-M greater than or equal to -1 is diffeomorphic to a Euclidean n-space R-n if the volume growth of geodesic balls in M is close to that of the balls in an n-dimensional hyperbolic space H-n(-1) of sectional curvature -1.