Volume Growth Estimates of Manifolds with Nonnegative Curvature Outside a Compact Set

Abstract

In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kähler manifolds with certain nonnegative holomorphic bisectional curvature and sectional curvature is at least half of the real dimension. The authors also give a brief proof of a generalized Yau's theorem.