Variants of Ahlfors' lemma and properties of the logarithmic potentials

边界上的新Schwarz-Pick引理与全纯映射的刚性

A new Schwarz-Pick Lemma at the boundary and rigidity of holomorphic maps

本文秉承Burns-Krantz边界Schwarz引理精神，利用Harnack型不等式和边界Hopf引理，为单位圆盘和$\mathbb C^N$强凸域上的共形伪度量与全纯自映射建立了新的边界Schwarz-Pick引理及刚性定理。

Logarithmic difference lemma in several complex variables and partial difference equations

In this paper, we mainly propose improvements of the logarithmic difference lemma for meromorphic functions in several complex variables, and then investigate meromorphic solutions of partial difference equations from the viewpoint of Nevanlinna theory.

对域闭合处对数双层势模连续性的估计

Estimates of the modulus of continuity of the logarithmic double layer potential in the closure of domain

本文基于Ahlfors正则积分曲线边界域，对Cauchy型积分实部的模连续性进行更精确的估计，通过构造例子验证估计的准确性。

A note on the asymptotic behavior of conformal metrics with negative curvatures near isolated singularities

The asymptotic behavior of conformal metrics with negative curvatures near an isolated singularity for at most second order derivatives was described by Kraus and Roth in one of their papers in 2008. Our work improves one estimate of theirs and shows the estimate for higher order derivatives near an isolated singularity by means of potential theory. We also give some limits of Minda-type for SK-metrics near the origin. Combining these limits with the Ahlfors' lemma, we provide some observations SK-metrics.

Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is presented and then applied to prove a number of results on meromorphic solutions of complex difference equations. These results include a difference analogue of the Clunie Lemma, as well as other results on the value distribution of solutions.

Logarithmic Comparison Theorem and Euler homogeneity for free divisors

This paper has been withdrawn by the author since the proof of Lemma 8 is not correct.

对数∂∂̄引理及其若干几何应用（附录与 Rao 共同撰写）

Logarithmic $\bf{\partial\bar\partial}$-lemma and several geometric applications (with an Appendix joint with Sheng Rao)

本文证明了紧致凯勒流形上的对数∂∂̄引理，并扩展了关于谱序列退化和变形的若干几何应用。

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.

Holomorphic curves in moduli spaces of polarized Abelian varieties

We study the value distribution of holomorphic curves from a general open Riemann surface into a smooth logarithmic pair $(X, D).$ By stochastic calculus, we first obtain a version of tautological inequality (proposed by McQuillan) and a logarithmic derivative lemma. Then, one uses them to establish a Second Main Theorem of Nevanlinna theory for pair $(X, D)$ under certain conditions. Finally, we apply the Second Main Theorem to study the holomorphic curves from a general open Riemann surface into certain special moduli spaces of polarized Abelian varieties intersecting boundary divisors.