Estimates for solutions of the $\partial$-equation and application to the characterization of the zero varieties of the functions of the nevanlinna class for lineally convex domains of finite type

Nevanlinna theory for holomorphic curves from annuli into semi Abelian varieties

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.

动态Nevanlinna-Pick理论、协变伸缩与非交换簇

Dynamic Nevanlinna-Pick Theory, Covariance Dilations, and Non-commutative Varieties

该研究推广了Nevanlinna-Pick插值理论，建立了相关算子理论框架，证明了H^∞(𝔻)成员关系的普遍检测方法，并揭示非交换内簇上Arveson型完全谱集表示失效的特性。

On holomorphic curves into complex projective varieties

In this paper, we study holomorphic curves satisfying the Fubini-Study derivative $\|f'(z)\|=O(|z|^σ)$ for some $σ>-1$ from the viewpoint of Nevanlinna theory

特征簇与对称双圆盘上的 Nevanlinna-Pick 插值问题

Distinguished varieties and the Nevanlinna-Pick interpolation problem on the symmetrized bidisk

本文研究对称双圆盘上可解 Nevanlinna-Pick 插值问题的唯一性集合，证明其为由插值数据规范构造的唯一性簇，并给出其中特征簇的完整代数与几何刻画。

Analytic Ax-Schanuel Theorem for semi-abelian varieties and Nevanlinna theory

The purpose of this paper is to explore Nevanlinna theory of the entire curve $\exh_A f:=(\exp_Af,f):\C \to A \times \Lie(A)$ associated with an entire curve $f: \C \to \Lie(A)$, where $\exp_A:\Lie(A)\to A$ is an exponential map of a semi-abelian variety $A$. Firstly we give a Nevanlinna theoretic proof to the {\em analytic Ax-Schanuel Theorem} for semi-abelian varieties, which was proved by J. Ax 1972 in the case of formal power series (Ax-Schanuel Theorem). We assume some non-degeneracy condition for $f$ such that the elements of the vector-valued function $f(z)-f(0) \in \Lie(A)\iso \C^n$ ar…

复拟射影簇的双曲性与基本群（I）：由 Nevanlinna 理论给出的极大拟 Albanese 维数

Hyperbolicity and fundamental groups of complex quasi-projective varieties (I): Maximal quasi-Albanese dimension by Nevanlinna theory

本文利用 Nevanlinna 理论，对定义在穿孔圆盘小分歧覆盖上、取值于极大拟 Albanese 维数且为对数一般型的复拟射影簇的全纯映射建立大 Picard 型定理，并由此证明广义 Green-Griffiths-Lang 猜想。