The Loewner equation for multiple slits, multiply connected domains and branch points

Abstract

Let \(\mathbb {D}\subset \mathbb {C}\) be the unit disk and let \(\gamma_{1},\gamma _{2}:[0,T]\to\overline{\mathbb {D}}\setminus\{0\}\) be parametrizations of two slits \(\Gamma_{1}:=\gamma(0,T], \Gamma_{2}:=\gamma_{2}(0,T]\) such that \(\Gamma_{1}\) and \(\Gamma_{2}\) are disjoint.