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Hölder regularity of the SLE trace
Author(s):
Joan
R.
Lind
Journal:
Trans. Amer. Math. Soc.
360
(2008),
3557-3578.
MSC (2000):
Primary 60D05, 30C35, 60G17
Posted:
January 9, 2008
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Abstract:
S. Rohde and O. Schramm have recently shown that the SLE trace is Hölder continuous (2005). However, their results are not optimal for all values of  and only yield a Hölder exponent near  for  near 0. In this paper, we give improved lower bounds on the optimal Hölder exponent for two natural parametrizations of the SLE trace. Our estimates give a Hölder exponent near 1 for  near 0, as expected. The work of I. Binder and B. Duplantier (2002) suggests that our results are optimal for the two parametrizations considered.
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Additional Information:
Joan
R.
Lind
Affiliation:
Department of Mathematics, Belmont University, 1900 Belmont Boulevard, Nashville, Tennessee 37212
DOI:
10.1090/S0002-9947-08-04327-4
PII:
S 0002-9947(08)04327-4
Received by editor(s):
February 24, 2005
Received by editor(s) in revised form:
April 22, 2006
Posted:
January 9, 2008
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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