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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Boundary behavior of SLE
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by Nam-Gyu Kang
J. Amer. Math. Soc. 20 (2007), 185-210
Published electronically: August 28, 2006


We show that the normalized (pre-)Schwarzian derivative of SLE, after we subtract a negligible term, is a complex BMO martingale. Its BMO norm gives strong evidence for Duplantier’s duality conjecture. We also show that it has correlations that decay exponentially in the hyperbolic distance. We reexamine S. Rohde and O. Schramm’s derivative expectation to derive the conjectured sharp estimate for the Hölder exponent unless the parameter of SLE is 4.
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Bibliographic Information
  • Nam-Gyu Kang
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 687219
  • ORCID: 0000-0003-4545-6899
  • Email:
  • Received by editor(s): January 31, 2005
  • Published electronically: August 28, 2006
  • Additional Notes: This research was partially conducted during the period when the author was employed by the Clay Mathematical Institute as a Liftoff Fellow. The author is partially supported by NSF grant DMS 05-05751.
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 20 (2007), 185-210
  • MSC (2000): Primary 30C45, 60K35; Secondary 28A80, 60J65
  • DOI:
  • MathSciNet review: 2257400