Harmonic measures of sides of a slit perpendicular to the domain boundary
type: Item
instance of: scholarly article
title: Harmonic measures of sides of a slit perpendicular to the domain boundary
zbMATH Open document ID: 1259.30008
author: Andrey Zakharov
author: Dmitri V. Prokhorov
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-08-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.4750
Mathematics Subject Classification ID: 30C35
Mathematics Subject Classification ID: 30C20
zbMATH DE Number: 6062860
zbMATH Keywords: chordal Löwner equation
zbMATH Keywords: singular solution
zbMATH Keywords: harmonic measure
reviewed by: David A. Brannan
MaRDI profile type: Publication
OpenAlex ID: W1979399366
arXiv ID: 1201.4750
cites work: Q3852455
cites work: Non-slit and singular solutions to the Löwner equation
cites work: Quasiconformal variation of slit domains
cites work: Q5527180
cites work: Exact solutions for Loewner evolutions
DOI: 10.1016/J.JMAA.2012.05.008
review text: Let the functions \(f(z,t)\), \(t\geq 0\), normalized near infinity by \(f(z, t)= z+ 2t/z+ O(1/z^2)\), map subdomains \(\mathbb{D}_t\) of the upper half-plane \(\mathbb{H}\) into \(\mathbb{R}\), and satisfy the chordal Löwner equation NEWLINE\[NEWLINE\frac{df(z, t)}{dt} =\frac{2}{f(z,t) \lambda(t)},NEWLINE\]NEWLINE where \(\lambda(t)\) is a continuous real-valued driving term.NEWLINENEWLINE In the case when the subdomains \(\mathbb{D}_t\) are a decreasing family consisting of \(\mathbb{H}\) minus an increasing vertical slit from the origin on \(\partial\mathbb{H}\), the authors show that the harmonic measures of the two sides of the slit are asymptotically equal. They also look at singular solutions of the chordal Löwner equation when the driving term has a higher Lipschitz order.
description: scientific article; zbMATH DE number 6062860