Ricci curvature, conjugate radius and large volume growth (Q1566386)

Let \((M,g)\) be an \(n\) dimensional complete non-compact Riemannian manifold whose Ricci curvature \(\rho\) is bounded from below by \(\rho\geq-(n-1)\). The author assumes that \((M,g)\) has large volume growth and establishes a topological rigidity theorem showing \(M\) must be diffeomorphic to Euclidean space. This result rests on an estimate for the criticality radius of such manifolds with positive conjugate radius and large volume growth.