Mean curvature flow with obstacles: existence, uniqueness and regularity of solutions

We show short time existence and uniqueness of ${\text{C}}^{1,1}$ solutions to the mean curvature flow with obstacles, when the obstacles are of class ${\text{C}}^{1,1}$. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.