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Generalized Levi Currents and Singular Loci for Families of Plurisubharmonic Functions
We show how the formalism of Levi currents on complex manifolds, as introduced by Sibony, can be used to study the analytic structure of singular...
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Continuity of the Perron–Bremermann envelope of plurisubharmonic functions
In this paper we are interested in studying the Perron–Bremermann envelope of plurisubharmonic functions. We give a sufficient condition for the...
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Envelope of plurisubharmonic functions in Cegrell’s classes
This paper aims to study the complex Monge–Ampère measure of an envelope of plurisubharmonic functions in Cegrell’s classes. We prove the Hölder...
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A Note on the Weighted Log Canonical Threshold of Toric Plurisubharmonic Functions
We prove a semicontinuity theorem for a class of certain weighted log-canonical thresholds of toric plurisubharmonic functions.
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The local properties of some subclasses of plurisubharmonic functions
The main aim of this note is first to give the definition of the local classes. It also aims at studying the local property of some subclasses of...
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Basics of q-Plurisubharmonic Functions
This chapter is partially extracted from the doctoral thesis and the collaborating papers of the second-named author together with E. S. Zeron. For...
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Lelong Number and the Log Canonical Thresholds of Plurisubharmonic Functions on Analytic Subsets
The aim of this paper is to introduce the notion of Lelong number and the log canonical thresholds of plurisubharmonic functions on analytic subsets A ...
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On the residual Monge–Ampère mass of plurisubharmonic functions with symmetry in \({{\mathbb {C}}}^2\)
The aim of this paper is to study the residual Monge–Ampère mass of a plurisubharmonic function with isolated singularity at the origin in
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A New Plurisubharmonic Capacity and Functions Holomorphic Along Holomorphic Vector Fields
The main purpose of this article is to present a generalization of Forelli’s theorem for functions holomorphic along a suspension of integral curves...
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Controlling Products of Currents by Higher Powers of Plurisubharmonic Functions
We discuss the existence of the current g k T, k ∈ ℕ for positive and closed currents T and unbounded plurisubharmonic functions g . Furthermore, a new...
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ON THE PROXIMATE ORDER WITH RESPECT TO THE MODEL FUNCTION
We investigate the generalization of the proximate order in the Valiron sense. The concept of proximate order is widely used in the theories of...
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Boundary points, minimal L2 integrals and concavity property II: Weakly pseudoconvex Kähler manifolds
In this paper, we consider minimal L 2 integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex Kähler manifolds with...