The pluricomplex Poisson kernel for strongly pseudoconvex domains

2020/07/13 by Filippo Bracci, Alberto Saracco, Bracci, Filippo +3
Mathematics · #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2007.06270

openalex publication_date 2020/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce, via a Phragmen-Lindelöf type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the \sl pluricomplex Poisson kernel because it shares many properties with the classical Poisson kernel of the unit disc. In particular, we show that such a function is continuous, it is zero on the boundary except at one boundary point where it has a non-tangential simple pole, and reproduces pluriharmonic functions. We also use such a function to obtain a new "intrinsic" version of the classical Julia's Lemma and Julia-Wolff-Carathéodory Theorem.

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