The rigidity of dimension estimate for holomorphic functions on K\"ahler manifolds

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.