The Holder continuity of SLE8 under Minkowski capacity parameterization
The Holder continuity problem of SLE8 is studied.Firstly,based on the SLEκ curve η is not locally 1/d-Holder continuous for κ∈(0,4],then the distortion theorem and Radon-Nikodym derivative are used to transform the two-sided full-plane SLEκ curve η into an exponential self-similar process with a fixed increment 1/d under Minkowski capacity parameter.Secondly,the self-similar SLE8 curve η with fixed increments are not 1/d-Holder continuous on any open interval,that is,the SLE8 curve η is not 1/d-Holder continuous on any open interval.The results can provide a reference for the Holder continuity of SLEκ.
Minkowski capacityparameterizationHolder continuitystopping time
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