On the Harmonic Measure and Capacity of Rational Lemniscates

Stamatis Pouliasis, Thomas Ransford

Research output: Contribution to journalArticle

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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.

Original languageEnglish
Pages (from-to)249-261
Number of pages13
JournalPotential Analysis
Volume44
Issue number2
DOIs
StatePublished - Feb 1 2016

Keywords

  • Harmonic measure
  • Lemniscates
  • Lindelöf principle
  • Logarithmic capacity
  • Rational functions

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