In this paper we consider the evolution of an isolated extremum of a function under the curvature motion in the plane. We define different notions of circular extrema and show that, immediately after the motion begins, the ...

We prove the existence of a bounded variation solution for a quasilinear elliptic problem involving the mean curvature operator and a sublinear nonlinearity. We obtain such a solution as the limit of the solutions of another ...

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 propose a modification in the usual numerical method for computing the solutions of the curvature equation in the plane . This modification takes place near the singularities of the image. We propose to ...

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 ...