Título: Maximum principles and consequences for translating solitons in fully nonlinear extrinsic geometric flows

Resumen: Extrinsic geometric flows serve as tools for deforming surfaces into others that satisfy a desired extrinsic geometric condition. For example, in the case of mean curvature flow, the initial data evolves in such a way that its area decreases, since it coincides with the gradient flow of the area functional.

In this talk, we will discuss a generalization of the mean curvature flow in which we consider deformations of a hypersurface in Euclidean space whose normal velocity is given by a scalar function evaluated at the principal curvatures. The class of functions  that we consider are symmetric, increasing in each variable, and homogeneous supported in an open symmetric cone.

In particular, we will focus on translating solitons, which correspond to self-similar deformations that move in a fixed unit direction. First, we will introduce the concepts of singularity models and their relevance for the classification of long-term deformations. We will then focus on techniques related to maximum principles to characterize the family of grim-reaper cylinder solitons, together with an obstruction result for strictly convex translating solitons contained in non-vertical round cylinders.