5 papers · 1 filter
Nevanlinna's five-value theorem on non-positively curved complete Kähler manifolds
Xianjing Dong
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 are identic…
On Griffiths conjecture
Xianjing Dong, Peichu Hu
By using techniques of holomorphic jets and Jacobian fields, we devise a non-equidistribution theory of holomorphic curves into complex projective varieties intersecting normal cro…
Fermat functional equations over Riemann surfaces
Xianjing Dong, Liangwen Liao, Kai Liu
We investigate the existence of non-trivial holomorphic and meromorphic solutions of Fermat functional equations over an open Riemann surface . When is hyperbolic, we prove…
Holomorphic curves whose domains are Riemann surfaces
Xianjing Dong
We establish a defect relation of holomorphic curves from a general open Riemann surface into a normal complex projective variety, with Zariski-dense image intersecting effective C…
Nevanlinna theory on complete Kähler manifolds
Xianjing Dong
We study Nevanlinna theory on complete Kähler manifolds. As a consequence of the main result, we prove a defect relation of holomorphic mappings from complete Kähler manifolds of n…