English

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