Sharp error analysis for curvature dependent evolving fronts

The evolution of a curvature dependent interface is approximated via a singularly perturbed parabolic double obstacle problem with small parameter epsilon > 0. The velocity normal to the front is proportional to its mean curvature plus a forcing term. Optimal interface error estimates of order O(epsilon2) are derived for smooth evolutions, that is before singularities develop. Key ingredients are the construction of sub(super)-solutions containing several shape corrections dictated by formal asymptotics, and the use of a modified distance function.