2023/08/31 by Xianjing Dong, Dong, Xianjing
Mathematics · #30D35 #32H30 #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2308.16520
openalex publication_date 2023/08/31 · openalex created_date 2023/09/03 · openalex updated_date 2026/07/28
Nevanlinna's five-value theorem is well-known as a famous theorem in value distribution theory, which asserts that two non-constant meromorphic functions on \mathbb C are identical if they share five distinct values ignoring multiplicities in \mathbb C. The central goal of this paper is to generalize Nevanlinna's five-value theorem to non-compact complete Kähler manifolds with non-positive sectional curvature by means of the theory of algebraic dependence. With a certain growth condition imposed, we show that two nonconstant meromorphic functions on such class of manifolds are identical if they share five distinct values ignoring multiplicities in \mathbb C.