Dimension Estimate of Polynomial Growth Holomorphic Functions

Abstract

On a complete noncompact Kähler manifold $M^{n}$ (complex dimension) with nonnegative Ricci curvature and Euclidean volume growth, we prove that polynomial growth holomorphic functions of degree d has an dimension upper bound $cd^{n}$, where c depends only on n and the asymptotic volume ratio. Note that the power is sharp.

Funding

Science and Technology Commission of Shanghai Municipality(18dz2271000); Program of Shanghai Academic/Technology Research Leader(20XD1401500)