We study curvature flows in the locally homogeneous case (e.g. compact quotients of Lie groups, solvmanifolds, nilmanifolds) in a unified way, by considering a generic flow under just a few natural conditions on the broad ...

In this work we have described the application of a machine learning strategy to compute the interface curvature in the context of a Front-Tracking framework. Based on angular information of normal and tangential vectors ...

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 ...

Recently, J. Streets and G. Tian introduced a natural way to evolve an almost-Kähler manifold called the symplectic curvature flow, in which the metric, the symplectic structure and the almost-complex structure are all ...

In this paper, we study the Ricci flow of solvmanifolds whose Lie algebra has an abelian ideal of codimension one, by using the bracket flow. We prove that solutions to the Ricci flow are immortal, the omega-limit of bracket ...

The aim of this paper is to study self-similar solutions to the symplectic curvature flow on 6-dimensional nilmanifolds. For this purpose, we focus our attention on the family of symplectic two- and three-step nilpotent ...