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A Dimension Estimate for Polynomial Growth Holomorphic Functions
Abstract
On a complete noncompact Kähler manifold Mn of complex dimension n with nonnegative Ricci curvature, we prove that polynomial growth holomorphic functions of degree d (d≥ 0) have an dimension upper bound C(n)(1+d)n. In particular, dimCOOd(M)≤ C'(n)dn, for d≥1, and the estimate is sharp.
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BibTeX
@misc{wang2026dimension,
title = {{A Dimension Estimate for Polynomial Growth Holomorphic Functions}},
author = {Haohao Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16174},
eprint = {2610.16174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16174},
}
RIS
TY - UNPB
TI - A Dimension Estimate for Polynomial Growth Holomorphic Functions
AU - Haohao Wang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16174
UR - https://arxiv.org/abs/2610.16174
AB - On a complete noncompact Kähler manifold M^n of complex dimension n with nonnegative Ricci curvature, we prove that polynomial growth holomorphic functions of degree d (d≥ 0) have an dimension upper bound C(n)(1+d)^n. In particular, dim_COO_d(M)≤ C'(n)d^n, for d≥1, and the estimate is sharp.
ER -