Continuity of the SLE trace in simply connected domains

2008/10/23 by Christophe Garban, Steffen Rohde, Garban, Christophe +3
Computer Science · Mathematics · Physics and Astronomy · #30C35 #60D05 #60G17 #60K35 #Advanced Mathematical Modeling in Engineering #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Probability (math.PR) #Spectral Theory in Mathematical Physics #math-ph #math.CV #math.MP #math.PR #msc:30C35 #msc:60D05 #msc:60G17 #msc:60K35

paper · pdf · doi:10.48550/arxiv.0810.4327

15 pages, 2 figures. Statement of theorem 1.2 corrected

openalex publication_date 2008/10/23 · arxiv created 2008/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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