A geometric flow on noncompact affine Riemannian manifolds

Abstract: In this paper, we obtain the existence criteria for a geometic flow on noncompact affine Riemannian manifolds. Our results can be regarded as a real version of Lee-Tam [19]. As an application, we prove that a complete noncompact Hessian manifold with nonnegative Hessian sectional curvature and bounded geometry is diffeomorphic to $\mathbb{R}^n$ if its tangent bundle has maximal volume growth.