Related papers: On plurisubharmonic defining functions for pseudoc…

We prove in an elementary way that for a Lipschitz domain $D\subset \cn$, all plurisubharmonic functions on $D$ can be regularized near any boundary point.

Recently the authors have explored new concepts of plurisubharmonicity and pseudoconvexity, with much of the attendant analysis, in the context of calibrated manifolds. Here a much broader extension is made. This development covers a wide…

Let $D^2 \subset C$ be a closed two-dimensional disk and $f:D^2 \to R$ be a continuous function such that a restriction of $f$ to $\partial D^2$ is a continuous function with a finite number of local extrema and $f$ has a finite number of…

In this paper, by modifying significantly the Friedrichs-Gross mollifier technique and/or using the Lasry-Lions regularization technique together with some carefully chosen cut-off functions, for the first time we construct explicitly…

We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…

Let $(M,\omega)$ be a Kahler manifold. An integrable function on M is called $\omega^q$-plurisubharmonic if it is subharmonic on all q-dimensional complex subvarieties. We prove that a smooth $\omega^q$-plurisubharmonic function is…

In this paper, we investigate the geometric properties of complex-valued pluriharmonic mappings defined over convex Reinhardt domains in $\mathbb{C}^n$. We first establish a multidimensional analogue of the Noshiro-Warschawski Theorem,…

In this paper we introduce, via a Phragmen-Lindel\"of type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the {\sl pluricomplex Poisson kernel} because it shares many properties with…

We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…

Given an unbounded strongly pseudoconvex domain D and a continuous real valued function h defined on bD, we study the existence of a (maximal) plurisubharmonic function u on D such that u=h on bD.

Given a negative plurisubharmonic function $\phi$ in a bounded pseudoconvex domain of ${\mathbb C}^n$, we introduce and study its residual function $g_\phi$ determined by the asymptotic behavior of $\phi$ near its singularity points, both…

Let $n \geq 4$ and let $\Omega$ be a bounded hyperconvex domain in $\mathbb{C}^{n}$. Let $\varphi$ be a negative exhaustive smooth plurisubharmonic function on $\Omega$. We show that any holomorphic function defined on a connected open…

In this paper, we introduce a concept of super-pseudoconvex domain. We prove that the solution of the Feffereman equation on a smoothly bounded strictly pseudoconvex domain $D$ in $\CC^n$ is plurisubharmonic if and only if $D$ is…

We extend a recent result of Avelin, Hed, and Persson about approximation of functions $u$ that are plurisubharmonic on a domain $\Omega$ and continuous on $\bar\Omega$, with functions that are plurisubharmonic on (shrinking) neighborhoods…

There exist several interesting results in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\C^n$. We introduce a…

We study proper holomorphic mappings between strictly pseudoconvex domains with low boundary regularity.

We prove that given a family of strictly pseudoconvex domains varying in C2 topology on domains, there exists a continuously varying family of exposing maps for all boundary points of all domains.

This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…

We construct a smoothly bounded pseudoconvex domain such that every boundary point has a p.s.h. peak function but some boundary point admits no (local) holomorphic peak function.

We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $\mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.