Continuity of the SLE trace in simply connected domains

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Garban, Christophe
Rohde, Steffen
Schramm, Oded
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Abstract
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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
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