2 citations · 2 across the 13 of their papers we have counts for
13 papers
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…
Nevanlinna theory on complete Kähler manifolds with non-negative Ricci curvature
Xianjing Dong
The paper develops an equidistribution theory of meromorphic mappings from a complete Kähler manifold with non-negative Ricci curvature into a complex projective manifold intersect…
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…
Nevanlinna theory via holomorphic forms
Xianjing Dong, Shuangshuang Yang
This paper re-develops the Nevanlinna theory for meromorphic functions on in the viewpoint of holomorphic forms. According to our observation, Nevanlinna's functions ca…
The Second Main Theorem for spherically symmetric Kähler manifolds
Xianjing Dong, Peichu Hu
We investigate the value distribution of holomorphic maps defined on one class of Kähler manifolds. With the very natural settings, we establish a Second Main Theorem which is of t…
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…
Algebraic degeneracy of holomorphic curves
Xianjing Dong, Peichu Hu
We consider the algebraic degeneracy of holomorphic curves from a point of view of meromorphic vector fields. Employing the notion of Jocabian sections introduced by W. Stoll, we e…
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…
Holomorphic curves in moduli spaces of polarized Abelian varieties
Xianjing Dong
We study the value distribution of holomorphic curves from a general open Riemann surface into a smooth logarithmic pair By stochastic calculus, we first obtain a version…
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…
H. Cartan's theory for Riemann surfaces
Xianjing Dong
We generalize the H. Cartan's theory of holomorphic curves for a general open Riemann surface. Besides, a vanishing theorem for jet differentials and a Bloch's theorem for Riemann…
Nevanlinna-type theory based on heat diffusion
Xianjing Dong
We obtain an analogue of Nevanlinna theory of holomorphic mappings from a complete and stochastically complete Kähler manifold into a complex projective manifold. When certain curv…
Carlson-Griffiths' theory via Brownian motion
Xianjing Dong
Early in 1970s, Carlson-Griffiths made a significant progress in the study of Nevanlinna theory, who devised equi-distribution theory for holomorphic mappings from in…