Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function

Convergence in Capacity of the Pluricomplex Green Function

In this paper we prove that if Ω is a bounded hyperconvex domain in C and if Ω 3 zj → ∂Ω, j → ∞, then the pluricomplex Green function gΩ(zj , ·) tends to 0 in capacity, as j →∞. A bounded open connected set Ω ⊂ Cn is called hyperconvex if there exists negative plurisubharmonic function ψ ∈ PSH(Ω) such that {z ∈ Ω : ψ(z) < c} ⊂⊂ Ω for all c < 0. Such ψ is called an exhaustion function for Ω. It ...

Computing the Pluricomplex Green Function with Two Poles

More accurate Jensen-type inequalities for signed measures characterized via Green function and applications

In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive. The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauch...

On the Regularity of the Pluricomplex Green Functions

Reduced functions and Jensen measures

Let φ be a locally upper bounded Borel measurable function on a Greenian open set Ω in Rd and, for every x ∈ Ω, let vφ(x) denote the infimum of the integrals of φ with respect to Jensen measures for x on Ω. Twenty years ago, B.J. Cole and T.J. Ransford proved that vφ is the supremum of all subharmonic minorants of φ on X and that the sets {vφ < t}, t ∈ R, are analytic. In this paper, a differen...