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arXiv · 1510.08124

On the harmonic measure and capacity of rational lemniscates

Stamatis Pouliasis·Thomas Ransford
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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's lemma for the capacity of the lemniscates of proper holomorphic functions.

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Stamatis Pouliasis, Thomas Ransford. 2015-10-27. On the harmonic measure and capacity of rational lemniscates. https://arxiv.org/abs/1510.08124

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