Dimension Estimate of Polynomial Growth Holomorphic Functions
Gang Liu
Peking Mathematical Journal ›› 2021, Vol. 4 ›› Issue (2) : 187 -202.
Dimension Estimate of Polynomial Growth Holomorphic Functions
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.
Science and Technology Commission of Shanghai Municipality(18dz2271000)
Program of Shanghai Academic/Technology Research Leader(20XD1401500)
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