Uniform convergence of Green's functions

Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is uniformly bounded.

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Bibliographic Details
Published in:arXiv.org 2017-05
Main Authors: Kalmykov, Sergei, Kovalev, Leonid V
Format: Article
Language:English
Subjects:
Convergence
Domains
Green's functions
Online Access:Get full text
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Description
Summary:Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is uniformly bounded.
ISSN:2331-8422
DOI:10.48550/arxiv.1705.02542