Speaker
Description
Self-similar shrinkers describe generic singularities of multiphase mean curvature flow at the parabolic scale. The classification of stable self-shrinkers, conjectured by Ilmanen, is a central step towards understanding global dynamics of generic flows. While the compact case of the circle is well understood at this point, classification of stable, non-compact shrinkers remains still open.
In this talk, we present a proof of the quantitave, nonlinear, local stability of the lens and three-ray star in terms of Huisken‘s F-entropy, completing the classification by covering all possible cases. The argument is based on a calibration technique together with a rigorous linearisation of the F-entropy. This is joint work with Julian Fischer and Theresa Simon.