9 papers
On Picard's Problem via Nevanlinna Theory II
Xianjing Dong
This work continues the author's earlier work (2026, Studia Mathematica) on Picard's problem: is every meromorphic function on a complete noncompact Kähler manifold with nonnegativ…
A Generalization of Zalcman's Lemma on Complex Lie Groups
Xianjing Dong, Yanda Lv, Lanjuan Xu
Zalcman's lemma makes significant applications in normal families, complex dynamics and many other related problems in complex analysis. It is interesting to explore a global versi…
Algebroid Mappings and Their Equidistribution Theory
Xianjing Dong
In this paper, the concept of algebroid mappings of complex manifolds is introduced based on that a large number of complex systems of PDEs admit multi-valued solutions that can be…
A refined form of the second main theorem on complete non-positively curved Kähler manifolds
Xianjing Dong
How to devise a second main theorem with best error terms is a central problem in the study of Nevanlinna theory. However, it seems difficult to be done for a general non-positivel…
Value distribution of meromorphic mappings on complete Kähler connected sums with non-parabolic ends
Xianjing Dong
All harmonic functions on possess Liouville's property, which is well-known as the Liouville's theorem. In 1979, Kuz'menko and Molchanov discovered a phenomenon that…
Unicity problem on meromorphic mappings of complete Kahler manifolds
Xianjing Dong, Mengyue Liu
Nevanlinna's unicity theorems have always held an important position in value distribution theory. The main purpose of this paper is to generalize the classical Nevanlinna's unicit…
Nevanlinna Theory on Geodesic Balls of Complete Kähler Manifolds
Xianjing Dong
We study Nevanlinna theory of meromorphic mappings from a geodesic ball of a general complete Kähler manifold with non-negative Ricci curvature into a complex projective manifold b…
On Picard's Problem via Nevanlinna Theory
Xianjing Dong
We consider the classical Picard's problem for non-parabolic complete Kähler manifolds with non-negative Ricci curvature. Based on the global Green function approach, we give a pos…
Nevanlinna Theory of Algebroid Functions on Complete Kähler Manifolds
Xianjing Dong
In this paper, we generalize the classical Nevanlinna theory of algebroid functions from to a complete Kähler manifold with either non-negative Ricci curvature or non-p…