Critical Measures and Parameter Space of Jenkins-Strebel Quadratic Differentials

Abstract

The thesis is devoted to applications of the theory of quadratic differentials to the problems of construction of critical measures, that provide critical values of the logarithmic energy of a charge system on the complex plane. We observe the properties of supports of such measures. We consider the problem of describing parameter space of Jenkins-Strebel differentials, which is related to the problem of describing critical measures.