English

Quadratic differentials A(z-a)(z-b)dz^2/(z-c)^2 and algebraic Cauchy transform

Classical Analysis and ODEs 2016-02-22 v2

Abstract

In this paper, we discuss the representability almost everywhere (a.e.) in the plane of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. We discuss the existence of critical trajectories of a family of quadratic differentials.

Keywords

Cite

@article{arxiv.1506.06543,
  title  = {Quadratic differentials A(z-a)(z-b)dz^2/(z-c)^2 and algebraic Cauchy transform},
  author = {Mohamed Jalel Atia and Faouzi Thabet},
  journal= {arXiv preprint arXiv:1506.06543},
  year   = {2016}
}

Comments

13 pages, 8 figures