On the regularity of SLE trace

Abstract

We revisit regularity of SLE trace, for all $\kappa \ne 8$, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia--Rodemich--Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index $\min (1+\kappa /8,2)$, improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.

arXiv comment16 pages, 4 figures. Comments are welcome