  We show that any open set that is a finite distance away from a Lipschitz
subgraph will become a Lipschitz subgraph after flowing under fractional mean
curvature flow for a finite, universal time. Our proof is quantitative and
inherently nonlocal, as the corresponding statement is false for classical mean
curvature flow. This is the first regularizing effect proven for weak solutions
to nonlocal curvature flow.
