Surfaces moving by Mean Curvature.

Abstract

We use a level-set method to describe surfaces moving by mean curvature. The interesting partial differential equation $u_t=|\nabla u| \text{div}\left(\frac{\nabla u}{|\nabla u|}\right)$ arises. In this thesis, we prove uniqueness of solutions in the viscosity sense and singularities of the flow are taken into consideration. Our work is based on the demanding proof of Evans and Spruck, published in Journal of Differential geometry (1991).