GAMP seminar by Francesco Chini (KU)

GAMP (Geometric Analysis and Mathematical Physics) Seminar.

Title: Translating Solitons and (Bi-)Halfspace Theorems for Minimal Surfaces

Abstract: I will present new results on the classification problem for complete self-translating hypersurfaces for the mean curvature flow. Such surfaces show up as models for Type II singularities in the flow and they can be characterized as minimal hypersurfaces with respect to a particular incomplete conformally flat metric.

Examples show that one cannot easily classify such solitons and not even their convex hulls.  However, we will show how to classify the convex hulls of the projection of self-translating solitons onto a particular hyperplane.  This classification implies several non-existence results for translating solitons already present in the literature. Our classification was inspired by a classical result of Hoffman-Meeks in 1990 for minimal submanifolds and the proof is based on an Omori-Yau Maximum Principle.

This is joint work with Niels Martin Møller (KU).