09.12.2021, 16:15
– Raum 2.9.0.12
Seminar Geometrie
The long neck principle
Rubens Longhi
Stephen Lynch
An important problem in mean curvature flow is to find conditions on initial data that rule out 'collapsing' singularity models, such as the Grim Reaper. This is a necessary step towards establishing regularity and compactness theorems for the flow. A prevalent class of singularity models are the convex ancient solutions. We will first discuss examples and general properties of such solutions, before moving on to a universality result (proven with T. Bourni and M. Langford) which asserts that a convex ancient solution is collapsing if and only if it admits a sequence of rescalings converging to a Grim Reaper. This makes it possible to rule out collapsing via curvature pinching.