Multipoint Estimates for Radial and Whole-plane SLE

We prove upper bounds for the probability that a radial SLE${}_{\kappa }$ curve, $\kappa \in (0,8)$, comes within specified radii of $n$ different points in the unit disc. Using this estimate, we then prove a similar upper bound for a whole-plane SLE${}_{\kappa }$ curve. We then use these estimates to show that the lower Minkowski content of both the radial and whole-plane SLE${}_{\kappa }$ traces restricted in a bounded region have finite moments of any order.