Capacitat analítica, aproximació i integrals singulars

The research project proposes to develop three research topics related to One Complex Variable, Potencial Theory and Singular Integrals: a) analytic capacity. The goal is to study the semiadditivity problem and the potencial theory of the Cauchy kernel; b) approximation by solutions of elliptic equations. We would like to use spectral synthesis to prove certain open problems in the theory; c) singular integrals on subsets of the plane. We intend to find new characterizations of uniform rectifiability.