On the Harmonic Measure and Capacity of Rational Lemniscates

Stamatis Pouliasis; Thomas Ransford

doi:10.1007/s11118-015-9508-z

On the Harmonic Measure and Capacity of Rational Lemniscates

Stamatis Pouliasis, Thomas Ransford

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study the lemniscates of rational maps. We prove a reflection principle for the harmonic measure of rational lemniscates and we give estimates for their capacity and the capacity of their components. Also, we prove a version of Schwarz’s lemma for the capacity of the lemniscates of proper holomorphic functions.

Original language	English
Pages (from-to)	249-261
Number of pages	13
Journal	Potential Analysis
Volume	44
Issue number	2
DOIs	https://doi.org/10.1007/s11118-015-9508-z
State	Published - Feb 1 2016

Keywords

Harmonic measure
Lemniscates
Lindelöf principle
Logarithmic capacity
Rational functions

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10.1007/s11118-015-9508-z

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abstract = "We study the lemniscates of rational maps. We prove a reflection principle for the harmonic measure of rational lemniscates and we give estimates for their capacity and the capacity of their components. Also, we prove a version of Schwarz{\textquoteright}s lemma for the capacity of the lemniscates of proper holomorphic functions.",

keywords = "Harmonic measure, Lemniscates, Lindel{\"o}f principle, Logarithmic capacity, Rational functions",

author = "Stamatis Pouliasis and Thomas Ransford",

note = "Funding Information: Research of second author supported by grants from NSERC and the Canada Research Chairs program. Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media Dordrecht.",

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AB - We study the lemniscates of rational maps. We prove a reflection principle for the harmonic measure of rational lemniscates and we give estimates for their capacity and the capacity of their components. Also, we prove a version of Schwarz’s lemma for the capacity of the lemniscates of proper holomorphic functions.

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KW - Lindelöf principle

KW - Logarithmic capacity

KW - Rational functions

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On the Harmonic Measure and Capacity of Rational Lemniscates

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Keywords

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