Related papers: Corrigendum: Conical plurisubharmonic measure and …
It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been…
It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.
In this paper, we mainly investigate distortion and covering theorems on some classes of pluriharmonic mappings.
A direct proof of Oka's lemma on the relation of holomorphic convexity and the properties of the distance to the boundary function is provided. Some related problems for subharmonicity properties of this function are also studied. A new…
In this paper, we study the existence of the tangent cone to a positive plurisubharmonic or plurisuperharmonic current with a suitable condition. Some Estimates of the growth of the Lelong functions associated to the current and to its…
In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to singularity theory but also to multiobjective optimization.
We give characterizations of (quasi-)plurisubharmonic functions in terms of $L^p$-estimates of $\bar\partial$ and $L^p$-extensions of holomorphic functions.
In this paper we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A holomorphic extension theorem (the version of the celebrated edge of the wedge theorem) will be given for this…
Given a bounded symmetric domain $D$, we study (positive) pluriharmonic functions on $D$ and investigate a possible analogue of the family of Clark measures associated with a holomorphic function from $D$ into the unit disc in $\mathbb C$.
We give a brief review of holomorphic motions and its relation with quasiconformal mapping theory. Furthermore, we apply the holomorphic motions to give new proofs of famous Konig's Theorem and Bottcher's Theorem in classical complex…
We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $\Omega$ -- both in one and several complex variables. The approach involves two new localized maximal functions. As a result of…
We discuss the behavior of harmonic functions on Riemannian cones as defined below and Lioville's theorem.
Let $f$ be a holomorphic function on the unit disc, and $(S_{n_{k}})$ be a subsequence of its Taylor polynomials about $0$. It is shown that the nontangential limit of $f$ and lim$_{k\rightarrow \infty }S_{n_{k}}$ agree at almost all points…
Two properties of plurisubharmonic functions are proven. The first result is a Skoda type integrability theorem with respect to a Monge-Amp\`ere mass with H\"older continuous potential. The second one says that locally, a p.s.h. function is…
In this paper we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion we prove an analogue of Blaschke-Privalov theorem for plurisubharmonic functions.
The aim of this paper is to present an extension theorem for the functions separately holomorphic on generalized (N,k)-crosses with pluripolar singularities.
We study boundary properties of plurisubharmonic functions near real submanifolds of almost complex manifolds.
The purpose of this paper is to study convergence of Monge-Ampere measures associated to sequences of plurisubharmonic functions defined on a hyperconvex subset of ${\mathbb C^n}$.
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…