关键词: Kahler manifold, holomorphic bisectional curvature, volume growth

Abstract:

In this article, using the properties of Busemann functions, the authors prove that the order of volume growth of Kahler 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.

Key words: Kahler manifold, holomorphic bisectional curvature, volume growth