Finite topology self-translating surfaces for the mean curva-ture flow constitute a key element in the analysis of TypeII singularities from a compact surface because they arise as lim-its after suitable blow-up scalings ...

In this article, we study eternal solutions to the Allen-Cahn equation in the 3-sphere, in view of the connection between the gradient flow of the associated energy functional, and the mean curvature flow. We construct ...

In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish ...

Finite topology self-translating surfaces for the mean curvature flow constitute a key element in the analysis of Type II singularities from a compact surface because they arise as limits after suitable blow-up scalings ...

Abstract In this paper we study the uniqueness of graphical mean curvature flow with locally Lipschitz initial data. We first prove that rotationally symmetric entire graphs are unique, without any further assumptions. Our ...

Mean curvature flow is a geometric flow that rises when evolving a hipersurface in the direction of its normal vector field with velocity at each point equal to the mean curvature at the very same point. As it is an evolution ...