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

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 $S^2$.