On the harmonic measure and capacity of rational lemniscates

2015/10/27 by Pouliasis, Stamatis, Ransford, Thomas · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.08124

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.

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• Rational lemniscates and the matching problem

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