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Hölder regularity of the SLE trace |
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| Authors: | Joan R. Lind |
| Affiliation: | Department of Mathematics, Belmont University, 1900 Belmont Boulevard, Nashville, Tennessee 37212 |
| 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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