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.
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Acknowledgements
The author would like to thank Professors Lei Ni, Gang Tian and Jiaping Wang for their interests and comments. He also thanks Professor Jean-Pierre Demailly for clarifying some points. Finally, he thanks the anonymous referees for improving the readability of the paper. The author was partially supported by NSFC No. 12071140, Program of Shanghai Academic/Technology Research Leader No. 20XD1401500, and the Science and Technology Commission of Shanghai Municipality No. 18dz2271000, as well as the Xplore Prize by Tencent.
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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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DOI: https://doi.org/10.1007/s42543-021-00034-w