Nevanlinna's five-value theorem on non-positively curved complete Kähler manifolds

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 $\bar{\mathbb{C}}\mathrm{.}$ 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 $\bar{\mathbb{C}}\mathrm{.}$