The rigidity of dimension estimate for holomorphic functions on K\"ahler manifolds
Differential Geometry
2026-03-26 v2
Abstract
In this paper, we obtain the optimal rigidity of dimension estimate for holomorphic functions with polynomial growth on K\"ahler manifolds with non-negative holomorphic bisectional curvature. There is a specific gap between the largest and the second largest dimension. We also determine the optimal dimension that ensures the maximal volume growth which implies the manifold is biholomorphic to the complex Euclidean space.
Cite
@article{arxiv.2510.14371,
title = {The rigidity of dimension estimate for holomorphic functions on K\"ahler manifolds},
author = {Jianchun Chu and Jie Deng and Zihang Hao and Jian Li},
journal= {arXiv preprint arXiv:2510.14371},
year = {2026}
}
Comments
26 pages; main result improved