Generic mean curvature flow with obstacles

Abstract

We study the obstacle problem associated to mean curvature flow. We add to the geometric vanishing-viscosity approximation of Evans and Spruck a singular perturbation that penalizes the violation of the constraint, and pass to the limit. The resulting level set formulation has unique solutions - up to fattening. Extending the work of Evans and Spruck and a work by Ullrich and one of the authors, we show that generic level sets of this flow are distributional solutions of the obstacle problem.