Year: 2026
Type: preprint
Abstract: 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 $d$ ($d\geq 0$) have an dimension upper bound $C(n)(1+d)^n$. In particular, $\dim_{\C}\OO_d(M)\leq C'(n)d^n,$ for $d\geq1$, and the estimate is sharp.
Source: arXiv (Cornell University)
Author: Wang, Haohao
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221771842