English

On the harmonic measure and capacity of rational lemniscates

Complex Variables 2015-10-29 v1

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.

Keywords

Cite

@article{arxiv.1510.08124,
  title  = {On the harmonic measure and capacity of rational lemniscates},
  author = {Stamatis Pouliasis and Thomas Ransford},
  journal= {arXiv preprint arXiv:1510.08124},
  year   = {2015}
}