The pluricomplex Poisson kernel for strongly pseudoconvex domains

强凸区域的复泊松核

The pluricomplex Poisson kernel for strongly convex domains

设$D$是$n$维复空间中的有界强凸区域.固定一点$p\in \partial D$，考虑在$p$上具有单极点的齐次复Monge-Ampere方程的解.证明了这样的解具有单位圆盘上经典泊松核的许多性质，因而称之为极点位于$p$的$D$的复泊松核.特别是，我们讨论的极值性质（如经典的Phragmen-Lindelof定理的推广），与多复格林函数的$D$的关系，在相关的叶理和边界表现和再生公式多重次调和函数方面的唯一性。

关于多复变量泊松核及其相关的复蒙日-安培方程

On the pluricomplex Poisson kernel and the associated complex Monge--Ampère equation

本文刻画了有界强线性凸域的多复变量泊松核，证实了Bracci等人的猜想，并构造一族连续解表明相关复蒙日-安培方程解不唯一，与格林函数情形形成对比。

凸有限型区域的多复变泊松核

The pluricomplex Poisson kernel for convex finite type domains

研究有界凸有限型区域上齐次复蒙日 - 安培方程的解 \(\Omega_\xi\)，基于度量和缩放技术，证明其性质，包括与多复变格林函数关系等，它是单位圆盘泊松核推广，还可用于强凸域，过程中建立了小林距离新估计。

Rooftop envelopes and residual plurisubharmonic functions

Given a negative plurisubharmonic function $ϕ$ in a bounded pseudoconvex domain of ${\mathbb C}^n$, we introduce and study its residual function $g_ϕ$ determined by the asymptotic behavior of $ϕ$ near its singularity points, both inside the domain and on its boundary. For certain choices of $ϕ$, the function $g_ϕ$ coincides with different versions of pluricomplex Green functions. The considerations are motivated by a problem on when two given plurisubharmonic functions can be connected by a plurisubharmonic geodesic.

强凸区域中的多势理论、半群和infinitesimal generators的边界表现

Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains

利用复格林函数和复泊松核刻画了强凸区域上全纯自映射半群的无穷小生成元.此外，我们还研究了半群的边界正则不动点。除其他外，我们的特点边界经常不动点的边界表现的无穷小发电机和在pluripotential理论。

Compactness of the $\bar{\partial}$-Neumann problem on domains with bounded intrinsic geometry

By considering intrinsic geometric conditions, we introduce a new class of domains in complex Euclidean space. This class is invariant under biholomorphism and includes strongly pseudoconvex domains, finite type domains in dimension two, convex domains, $\mathbb{C}$-convex domains, and homogeneous domains. For this class of domains, we show that compactness of the $\bar{\partial}$-Neumann operator on $(0,q)$-forms is equivalent to the boundary not containing any $q$-dimensional analytic varieties (assuming only that the boundary is a topological submanifold). We also prove, for this class of d…