Gaussian Mean curvature flow

Abstract

We consider the evolution of a $n$-dimensional convex hypersurface in the euclidean space under mean curvature flow with densities $e^{\epsilon \frac{1}{2}n{\mu }^2|x{|}^2}$, $\epsilon =\pm 1$, and completely determine it depending on the relation between $\mu$ and the upper or lower bound of the normal curvatures of the evolving hypersurface at time 0.

10 pages