Construction of High Codimension Ancient Mean Curvature Flows

2019/08/07 by Stryker, Douglas, Sun, Ao
#53C44 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.02688

Abstract

We construct a class of compact ancient solutions to the mean curvature flow in Euclidean space with high codimension. In particular, we construct higher codimensional ancient curve shortening flows. Moreover, we characterize the asymptotic behavior of these solutions. Add on remark: the construction in this paper has been discovered by Altschuler D.-Altschuler S.-Angenent-Wu in [AAAW13].

Related

• Pinched Ancient Solutions to the High Codimension Mean Curvature Flow
• Codimension Bounds and Rigidity of Ancient Mean Curvature Flows by the Tangent Flow at -∞
• Curvature estimates of ancient solutions to the mean curvature flow of higher codimension with convex Gauss image
• Mean curvature flow in higher codimension - Introduction and survey
• Convex ancient solutions to mean curvature flow