Dynamical stability of various convex graphical translators

Abstract

In the first part of the paper, we prove the existence of longtime solution to mean curvature flow starting from a graph of a continuous function defined over a slab. Then, we establish dynamical stability results for various types of graphical translators to mean curvature flow, namely the grim reaper, two dimensional graphical translators, and asymptotically cylindrical translators.

Comments welcome. Added a corollary imposing an entropy bound assumption instead of mean convexity in asymptotically cylindrical case