Continuity of the SLE trace in simply connected domains

Abstract

We prove that the $SL{E}_{\kappa }$ trace in any simply connected domain $G$ is continuous (except possibly near its endpoints) if $\kappa <8$. We also prove an SLE analog of Makarov's Theorem about the support of harmonic measure.

15 pages, 2 figures. Statement of theorem 1.2 corrected