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