A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature

Details A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature

2003-07-21

arxiv.org/abs/math/0307275v1

Mathematics

Differential Geometry

Scientific paper

In this paper, we derive a new monotonicity formula for the plurisuhbarmonic
functions on complete K\"ahler 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.

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