Geometric Analysis Seminar

speaker: Stephen Lynch (Tubingen University)

title: Convex ancient solutions of mean curvature flow with Type I curvature growth

abstract: Solutions of mean curvature flow that exist for all negative times (ancient solutions) are of fundamental importance, in part because they arise as blow-up limits at singularities. We will show that every convex ancient solution of Type I (meaning its curvature grows like that of a shrinker) is in fact a family of homothetically shrinking cylinders. The argument does not make use of Huisken's monotonicity formula, and so can be applied to a wide range of fully nonlinear flows as well.