These notes provide an introduction to translating solitons for the mean curvature flow in \(\mathbf {R}^3\). In particular, we describe a full classification of translators that are complete graphs over domains {R}^2\).

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 sensitivi...