Holomorphic Functions on a Class of Kähler Manifolds With Nonnegative Curvature, I

Abstract

Abstract In this paper, we consider holomorphic functions of polynomial growth on complete Kähler manifolds with nonnegative curvature. We explain how their growth orders are related to the asymptotic behavior of Kähler–Ricci flow. The main result is to determine minimal orders of holomorphic functions on gradient Kähler–Ricci expanding solitons with nonnegative Ricci curvature.