A monotonicity formula on complete K\"ahler manifolds with nonnegative bisectional curvature
classification
🧮 math.DG
math.CV
keywords
ahlerbisectionalcompletecurvaturederiveformulafunctionsmanifolds
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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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