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arXiv · 1506.06543

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

Mohamed Jalel Atia·Faouzi Thabet
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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.

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Mohamed Jalel Atia, Faouzi Thabet. 2016-02-19. Quadratic differentials A(z-a)(z-b)dz^2/(z-c)^2 and algebraic Cauchy transform. https://arxiv.org/abs/1506.06543

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