Analytic capacity and holomorphic motions
Complex Variables
2020-11-24 v1 Dynamical Systems
Abstract
We study the behavior of the analytic capacity of a compact set under deformations obtained by families of conformal maps depending holomorphically on the complex parameter. We show that, under those deformations, the logarithm of the analytic capacity varies harmonically. We also show that the hypotheses in this result cannot be substantially weakened.
Keywords
Cite
@article{arxiv.2011.11508,
title = {Analytic capacity and holomorphic motions},
author = {Stamatis Pouliasis and Thomas Ransford and Malik Younsi},
journal= {arXiv preprint arXiv:2011.11508},
year = {2020}
}