Related papers: Subextension of plurisubharmonic functions with we…
We prove that a relatively compact pseudoconvex domain with smooth boundary in an almost complex manifold admits a bounded strictly plurisubharmonic exhaustion function. We use this result for the study of convexity and hyperbolicity…
Our interest is the behavior of weak geodesics between two plurisubharmonic functions on pseudoconvex domains. We characterize the convergence condition along the geodesic between toric psh functions with a pole at origin on a unit ball in…
We study the problem of the existence and the holomorphicity of the Monge-Amp\`ere foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Amp\`ere equation even at points of arbitrary degeneracy. We obtain…
We study swept-out Monge-Ampere measures of plurisubharmonic functions and boundary values related to these measures.
We present some results dealing with the local geometry of almost complex manifolds. We establish mainly the complete hyperbolicity of strictly pseudoconvex domains, the extension of plurisubharmonic functions through generic submanifolds…
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.
We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in $\mathbb{C}^2$. In particular, we construct a family of simple counterexamples to the existence of…
We discuss pluripotential aspects of the Monge-Amp\`ere equations on compact Hermitian manifolds and prove $L^{\infty}$ estimates for any metric, as well as the existence of weak solutions under an extra assumption.
We study the minimum sets of plurisubharmonic functions with strictly positive Monge-Amp\`ere densities. We investigate the relationship between their Hausdorff dimension and the regularity of the function. Under suitable assumptions we…
We show that a recent result of Demailly and Pham Hoang Hiep \cite{DH} implies a description of plurisubharmonic functions with given Monge-Amp\`ere mass and smallest possible log canonical threshold. We also study an equality case for the…
Let $n \geq 3$ and $\Omega$ be a bounded domain in $\mathbb{C}^n$ with a smooth negative plurisubharmonic exhaustion function $\varphi$. As a generalization of Y. Tiba's result, we prove that any holomorphic function on a connected open…
In this note, we study the approximation of singular plurifinely plurisubharmonic function $u$ defined on a plurifinely domain $\Omega$. Under some conditions, we prove that $u$ can be approximated by an increasing sequence of…
A notion of indicator for a plurisubharmonic function u of logarithmic growth in C^n is introduced and studied. It is applied to evaluation of the total Monge-Amp\`ere measure (dd^cu)^n({C}^n). Upper bounds for the measure are obtained in…
We prove that a plurisubharmonic function on a domain in the complex Euclidean space is a locally VMO (Vanishing Mean Oscillation) function if and only if its Lelong number at each point vanishes. We also give a global version of this…
We prove some results which give sufficient conditions so that pointwise approximation of negative plurisubharmonic functions on complex varieties by continuous plurisubharmonic ones is possible.
Let A be an integral Banach ring, and X/A be a projective scheme of finite type, endowed with a semi-ample line bundle L. We define a class PSH(X,L) of plurisubharmonic metrics on L on the Berkovich analytification X^an and prove various…
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…
We construct examples of plurisubharmonic functions with isolated singularities at $0\in \mathbb{C}^n$, whose residual Monge-Amp\`{e}re masses at the origin can not be approximated by masses of analytic approximations obtained via…
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 ${\mathbb C^n}$.
In this paper, we combine tools from pluripotential theory and commutative algebra to study singularity invariants of plurisubharmonic functions. We establish several relationships between the singularity invariants of plurisubharmonic…