The pluricomplex Poisson kernel for strongly convex domains

2005/07/12 by Filippo Bracci, Bracci, Filippo, Giorgio Patrizio +3 · 1 citation
Mathematics · #32U35 #32W20 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #math.AP #math.CV #msc:32U35 #msc:32W20

paper · pdf · doi:10.48550/arxiv.math/0507247

31 pages

arxiv created 2005/07/12 · arxiv updated 2009/12/01

Abstract

Let D be a bounded strongly convex domain in the complex space of dimension n. Fixed a point p∈ ∂ D, we consider the solution of a homogeneous complex Monge-Ampere equation with simple pole at p. We prove that such a solution enjoys many properties of the classical Poisson kernel in the unit disc and thus deserves to be called the pluricomplex Poisson kernel of D with pole at p. In particular we discuss extremality properties (such as a generalization of the classical Phragmen-Lindelof theorem), relations with the pluricomplex Green function of D, uniqueness in terms of the associated foliation and boundary behaviors and reproducing formulas for plurisubharmonic functions.

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