Nonfattening of Mean Curvature Flow at Singularities of Mean Convex Type |
| |
Authors: | Or Hershkovits Brian White |
| |
Affiliation: | Department of Mathematics, Stanford University, 450 Serra Mall, Stanford, CA, 94304 USA |
| |
Abstract: | We show that a mean curvature flow starting from a compact, smoothly embedded hypersurface M ⊆ ℝn + 1 remains unique past singularities, provided the singularities are of mean convex type, i.e., if around each singular point, the surface moves in one direction. Specifically, the level set flow of M does not fatten if all singularities are of mean convex type. We further show that assumptions of the theorem hold provided all blowup flows are of the kind appearing in a mean convex flow, i.e., smooth, multiplicity 1 , and convex. Our results generalize the well-known fact that the level set flow of a mean convex initial hypersurface M does not fatten. They also provide the first instance where nonfattening is concluded from local information around the singular set or from information about the singularity profiles of a flow. © 2019 Wiley Periodicals, Inc. |
| |
Keywords: | |
|
|