Aarhus Universitets segl

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

Niels Martin Møller (Copenhagen University)
Onsdag 28. november 2018 14:15–15:15 Aud. D4 (1531-219)

I will present new results on the classification problem for complete self-translating hypersurfaces for the mean curvature flow. Such surfaces show up as singularity models in the flow (along with other types of solitons, e.g. the self-shrinkers), and have been studied since the first examples were found by Mullins in 1956.

Examples from gluing constructions show that one cannot easily classify such solitons - nor can one classify their projections to one dimension lower, nor their convex hulls. But if one does both of these "forgetful" operations, the list becomes very short, coinciding with (and implying) the one given by Hoffman-Meeks in 1989 for minimal submanifolds: All of $R^n$, halfspaces, slabs, hyperplanes and convex compacts in $R^n$. This also implies several of the known obstructions to existence, e.g. for convex translating solitons.

This is joint work with Francesco Chini (U Copenhagen).

Organiseret af: QGM
Kontakt: Cristiano Spotti, Martin de Borbon & Roberta Iseppi Revideret: 09.03.2020