Continuity of the SLE trace in simply connected domains
Christophe Garban, Steffen Rohde, Oded Schramm · arXiv (Cornell University) · 2008
We prove that the $SLE_κ$ trace in any simply connected domain $G$ is continuous (except possibly near its endpoints) if $κ<8$. We also prove an SLE analog of Makarov's Theorem about the support of harmonic measure.