Harmonic measures supported on curves
type: Item
instance of: scholarly article
title: Harmonic measures supported on curves
zbMATH Open document ID: 0677.30017
author: Lennart Carleson
author: Peter Jones
author: Christopher J. Bishop
author: John B. Garnett
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pjm/1102650148
review text: The following nice result is proved: Let \(\Omega_ 1\), \(\Omega_ 2\) be the two complementary domains of a Jordan curve \(\Gamma\) in the complex plane and let \(\omega_ 1\), \(\omega_ 2\) be the harmonic measures on \(\Gamma\) for the two regions \(\Omega_ 1\), \(\Omega_ 2\) with respect to two given points \(z_ 1\in \Omega_ 1\) and \(z_ 2\in \Omega_ 2\). Then (1) and (2) below are equivalent: (1) \(\omega_ 1\perp \omega_ 2\); (2) \(T_ 1\cap T_ 2\) has zero length (1-dimensional Hausdorff measure) where \(T_ j\) is the set of inner tangent points with respect to \(\Omega_ j\); \(j=1,2\).
Mathematics Subject Classification ID: 30C85
Mathematics Subject Classification ID: 31A15
zbMATH DE Number: 4109087
zbMATH Keywords: Jordan domain
zbMATH Keywords: inner tangent points
zbMATH Keywords: harmonic measures
reviewed by: B. Øksendal
MaRDI profile type: Publication
OpenAlex ID: W1988870367
DOI: 10.2140/PJM.1989.138.233
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description: scientific article; zbMATH DE number 4109087