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Original Article

Dimension Estimate of Polynomial Growth Holomorphic Functions

School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai 200241, China
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Abstract

On a complete noncompact Kähler manifold Mn (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 cdn, where c depends only on n and the asymptotic volume ratio. Note that the power is sharp.

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Peking Mathematical Journal
Pages 187-202
Cite this article:
Liu, G. Dimension Estimate of Polynomial Growth Holomorphic Functions. Peking Math J 4, 187-202 (2021). https://doi.org/10.1007/s42543-021-00034-w
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