Optimal control of volume-preserving mean curvature flow

We develop a framework and numerical method for controlling the full space-time tube of geometrically driven flow. consider an optimal control problem mean curvature flow curve or surface with volume constraint, where parameter acts as forcing term in motion law. The trajectory is achieved by minimizing appropriate tracking-type cost functional. gradient functional obtained via formal sensitivity analysis generated show that perturbation may be described transverse field satisfying parabolic equation on tube. propose algorithm to approximate several results two three dimensions demonstrating efficiency approach.