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 non-positive sectional curvature into complex projective manifolds under certain growth condition.
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Hyperbolicity properties of moduli spaces of marked hyperk{ä}hler manifolds
研究标记超kähler流形模空间的双曲性性质，证明Kobayashi伪距离消失，并推广Greb和Schwald的定理到任意维数和非紧曲线情况。
The goal of this short note is to point out that every Fano manifold with a nef tangent bundle possesses an almost K{ä}hler-Einstein metric, in a weak sense. The technique relies on a regularization theorem for closed positive (1, 1)-currents. We also discuss related semistability questions and Chern inequalities.
Using the theory of totally real number fields we construct a new class of compact complex non-K{ä}hler manifolds in every even complex dimension and study their analytic and geometric properties.
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 curvature conditions are imposed, the Nevanlinna-type defect relation based on heat diffusion is derived.
Exponential mixing of all orders and CLT for automorphisms of compact K{ä}hler manifolds
本文研究上同调作用简单的紧 Kähler 流形自同构，证明其唯一最大熵测度对 Hölder 可观测量具有所有阶指数混合性，并推出 CLT，结果覆盖所有正熵紧 Kähler 曲面自同构。
Nevanlinna Theory of Algebroid Functions on Complete Kähler Manifolds
本文将经典代数体函数Nevanlinna理论从复平面推广至具有非负Ricci曲率或非正截面曲率的完备Kähler流形，并以此建立了Picard型与五值型定理。
Nevanlinna's five-value theorem on non-positively curved complete Kähler manifolds
本文通过代数相关性理论，将Nevanlinna五值定理推广到非正截面曲率的非紧完备Kähler流形，在增长条件下证明两个非常数亚纯函数若忽略重数分担五个不同值则恒等。
On Picard's Problem via Nevanlinna Theory
研究非抛物完全凯勒流形在非负曲率下的皮卡问题，利用全局格林函数方法，证明若满足体积增长条件，则任一全纯函数若避开三个不同值则为常数，且非多项式增长的全纯函数最多避开两个值。
Nevanlinna Second Main Theorem and tautological inequality for parabolic manifolds
本文研究抛物流形到光滑射影流形的全纯映射，建立第二基本定理型不等式，并为光滑对数对导出抛物重言不等式。
Nevanlinna Theory on Geodesic Balls of Complete Kähler Manifolds
本文通过热核方法，在非负Ricci曲率的完备Kähler流形上推广了Nevanlinna第二主要定理，并得到Picard定理。
Nevanlinna theory on complete Kähler manifolds with non-negative Ricci curvature
该研究在非负Ricci曲率的完备Kähler流形框架下发展亚纯映射的Nevanlinna等分布理论，得到带精细误差的第二基本定理、精确亏量关系，还推广了五值定理等多个唯一性结果。
The purpose of this article is threefold. The first is to construct a Nevanlina theory for meromorphic mappings from a polydisc to a compact complex manifold. In particular, we give a simple proof of Lemma on logarithmic derivative for nonzero meromorphic functions on $\mathbb{C}^l.$ The second is to improve the definition of the non-integrated defect relation of H. Fujimoto \cite{F2} and to show two theorems on the new non-integrated defect relation of meromorphic maps from a closed submanifold of $\mathbb{C}^l$ to a compact complex manifold. The third is to give a unicity theorem for meromor…
We study pluripotential complex Monge-Ampère flows in big cohomology classes on compact K{ä}hler manifolds. We use the Perron method, considering pluripotential subsolutions to the Cauchy problem. We prove that, under natural assumptions on the data, the upper envelope of all subsolutions is continuous in space and semi-concave in time, and provides a unique pluripotential solution with such regularity. We apply this theory to study pluripotential K{ä}hler-Ricci flows on compact K{ä}hler manifolds of general type as well as on stable varieties.
A note on the transcendental basepoint-free conjecture for Calabi-Yau manifolds
本文证明Calabi-Yau流形的超越无基点猜想在其Beauville-Bogomolov分解的超Kähler因子上成立时即成立，并利用Bakker-Lehn收缩定理在超Kähler流形上给出该猜想成立的一个充分条件。
On Picard's Problem via Nevanlinna Theory II
本文基于皮卡问题，探讨非紧致凯勒流形上全纯函数的性质，通过全局格林函数方法解决非抛物情况，引入热核方法发展卡尔松-格里菲斯理论，验证抛物情况下的皮卡问题。
In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into Kähler compact manifold and. As its application, a second main theorem for holomophic curves from annuli into semi abelian varieties intersecting with only one divisor is given.
Unicity problem on meromorphic mappings of complete Kahler manifolds
本文将经典奈望林纳唯一性定理推广到具有非正截面曲率或非负里奇曲率的非紧完备凯勒流形上，拓展了值分布理论的适用范围。
We develop a parabolic pluripotential theory on compact K{ä}hler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Amp{è}re equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the K{ä}hler-Ricci flow on varieties with log terminal singularities.
We show that any fibration of a 'special' compact K{ä}hler manifold X onto an Abelian variety has no multiple fibre in codimension one. This statement strengthens and extends previous results of Kawamata and Viehweg when $κ$(X) = 0. This also corrects the proof given in [2], 5.3 which was incomplete.
A refined form of the second main theorem on complete non-positively curved Kähler manifolds
针对一般非正曲率Kähler流形上第二主定理误差项难以优化的问题，基于A. Atsuji的工作，利用良好估计提出了亚纯映射第二主定理的精化形式，改进了2018年的误差项结果。
Entire curves in C-pairs with large irregularity
本文推广Bloch-Ochiai定理至C-对，证明具有大不规则性的C-对中无稠密整C-曲线，并适用于任意奇点的正规Kähler对，基于Kawamata、Ueno和Noguchi的工作重构抛物Nevanlinna理论。
Value distribution of meromorphic mappings on complete Kähler connected sums with non-parabolic ends
针对带非抛物端的完备Kähler连通和上调和函数Liouville性质的刚性问题，研究其上到复射影流形的亚纯映射值分布，建立几何条件下的Nevanlinna理论第二基本定理，证明体积增长条件下Cauchy-Riemann方程可保证该性质的刚性。
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