The spherical Minkowski content and natural parametrization on the sphere for the Schramm-Loewner evolution

Tianyu Wei, Wanyang Dai

Published 2022-11-11Version 1

Studying SLE$_{\kappa}$ on $S^2$ provides a new and interesting perspective for the conformality of some 2-dimensional physical models. We prove the existence and some basic properties of the spherical Minkowski content of SLE$_{\kappa}$, which is finite and can be viewed as the natural parametrization of SLE$_{\kappa}$ on $S^2$.