Computation of Analytic Capacity and applications to the Subadditivity Problem
Complex Variables
2015-12-17 v2
Abstract
We develop a least-squares method for computing the analytic capacity of compact plane sets with piecewise-analytic boundary. The method furnishes rigorous upper and lower bounds which converge to the true value of the capacity. Several illustrative examples are presented. We are led to formulate a conjecture which, if true, would imply that analytic capacity is subadditive. The conjecture is proved in a special case.
Keywords
Cite
@article{arxiv.1209.3326,
title = {Computation of Analytic Capacity and applications to the Subadditivity Problem},
author = {Malik Younsi and Thomas Ransford},
journal= {arXiv preprint arXiv:1209.3326},
year = {2015}
}
Comments
41 pages, to appear in Comput. Methods Funct. Theory