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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…