## Continuity of the SLE trace in simply connected domains

##### Authors
Garban, Christophe
Rohde, Steffen
Schramm, Oded
##### Description
We prove that the $SLE_\kappa$ 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.
Comment: 15 pages, 2 figures. Statement of theorem 1.2 corrected
##### Keywords
Mathematics - Probability, Mathematical Physics, Mathematics - Complex Variables, 60G17, 30C35, 60K35, 60D05