Minkowski content and natural parameterization for the Schramm-Loewner   evolution
  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. 
Gregory F. Lawler, Mohammad A. Rezaei
math.PR