Complex Hessian equations with prescribed singularity on compact Kähler manifolds

双曲性性质的标记超kähler流形模空间

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。

具有给定奇点的复 Hessian 方程的相对有限能量类

Relative Finite Energy Classes for Complex Hessian Equations with Prescribed Singularities

本文针对具有给定奇点的复 Hessian 方程，引入相对有限能量类并建立相对比较原理，从而证明解的唯一性及一大类测度下方程的存在唯一性。

紧致 Hermitian 流形上复 Hessian 方程解的连续性

Continuity of solutions to complex Hessian equations on compact Hermitian manifolds

本文在紧致 Hermitian 流形上，通过 Orlicz 空间中的正右端项假设获得 $L^\infty$ 估计，进而证明复 Hessian 方程连续解的存在性。

Weighted Green functions for complex Hessian operators

Let $1\leq m\leq n$ be two fixed integers. Let $Ω\Subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and $\mathcal A \subset Ω\times ]0,+ \infty[$ a finite set of weighted poles. We define and study properties of the $m$-subharmonic Green function of $Ω$ with prescribed behaviour near the weighted set $A$. In particular we prove uniform continuity of the exponential Green function in both variables $(z,\mathcal A)$ in the metric space $\bar Ω\times \mathcal F$, where $\mathcal F$ is a suitable family of sets of weighted poles in $Ω\times ]0,+ \infty[$ endowed with the Hausdorff distance. …

$\bar\partial$-问题在$Z(q)$-域上

The $\bar\partial$-problem on $Z(q)$-domains

研究$Z(q)$-域中$\bar\partial$-问题的$L^2$上同调消失条件，通过构造光滑权重函数和Levi形式与复Hessian的交互条件。