Asymptotic convergence of evolving hypersurfaces

Carlo Mantegazza, Marco Pozzetta

If $\psi :M^n\to {\mathbb{R}}^{n+1}$ is a smooth immersed closed hypersurface, we consider the functional ${\mathcal{F}}_m(\psi )={\int }_{M}1+|{\nabla }^m\nu {|}^{2}d\mu$, where $\nu$ is a local unit…