8 papers · 1 filter
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
Zalcman's Lemma makes significant applications in normal families, complex dynamics and related problems in complex analysis. In the present paper, we are devoted to generalizing t…
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…
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…