Explicit Loewner flows and their geometry

Sammanfattning: In this Licentiate Thesis, we address problems related to partialdifferential equations for Loewner Theory. We studymulti-slit Loewner flows in the unit disc and the upper half planerespectively. Specifically, we solve explicitly Loewner’s PDE for aparticular choice of driving functions and we describe the geometry ofthese solutions, while we also remark a close connection of these solutions to semigroups of holomorphic self maps.To conclude, we present a short note onelementary examples of Loewner flows, driven by time-dependent densities.