Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at -∞

2019/09/05 by Stryker, Douglas, Sun, Ao
#53C44 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.02535

Abstract

Motivated by the limiting behavior of an explicit class of compact ancient curve shortening flows, we prove codimension bounds for ancient mean curvature flows by their tangent flow at -∞, generalizing a theorem for cylinders in [CM19b]. In the case of the m-covered circle, we apply this bound to prove a strong rigidity theorem. Furthermore, we extend this paradigm by showing that under the assumption of sufficiently rapid convergence, a compact ancient mean curvature flow is identical to its tangent flow at -∞.

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