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

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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