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math.CV2025
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…
math.CV2025
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…
math.CV2025
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…