Minkowski content and natural parameterization for the Schramm-Loewner evolution

Gregory F. Lawler; Mohammad A. Rezaei

doi:10.1214/13-AOP874

Minkowski content and natural parameterization for the Schramm-Loewner evolution

Probability 2015-06-22 v2

Authors: 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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@article{arxiv.1211.4146,
  title  = {Minkowski content and natural parameterization for the Schramm-Loewner evolution},
  author = {Gregory F. Lawler and Mohammad A. Rezaei},
  journal= {arXiv preprint arXiv:1211.4146},
  year   = {2015}
}

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Published at http://dx.doi.org/10.1214/13-AOP874 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Minkowski content and natural parameterization for the Schramm-Loewner evolution

Abstract

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