A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature

Abstract

In this paper, we derive a new monotonicity formula for the plurisuhbarmonic functions on complete Kähler manifolds with nonnegative bisectional curvature. As applications we derive the sharp estimates for the dimension of the spaces of holomorphic functions (sections) with polynomial growth, which in particular, partially solve a conjecture of Yau.