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arXiv · 1211.4146

Minkowski content and natural parameterization for the Schramm-Loewner evolution

Gregory F. Lawler·Mohammad A. Rezaei
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Abstract

We prove the existence and nontriviality of the $d$-dimensional 4 Minkowski content for the Schramm-Loewner evolution ($\mathrm {SLE}_{\kappa}$) with $\kappa<8$ and $d=1+\frac{\kappa}{8}$. We show that this is a multiple of the natural parameterization.

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Gregory F. Lawler, Mohammad A. Rezaei. 2012-11-17. Minkowski content and natural parameterization for the Schramm-Loewner evolution. https://doi.org/10.1214/13-aop874

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