LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS

On the Regularity of the Pluricomplex Green Functions

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

Partial pluricomplex energy and integrability exponents of plurisubharmonic functions

We give a sufficient condition on the Monge-Ampère mass of a plurisubharmonic function u for exp(−2u) to be locally integrable.

Hypercomplex Limits of Pluricomplex Structures and the Euclidean Limit of Hyperbolic Monopoles

We discuss the Euclidean limit of hyperbolic SU(2)-monopoles, framed at infinity, from the point of view of pluricomplex geometry. More generally, we discuss the geometry of hypercomplex manifolds arising as limits of pluricomplex manifolds.