On a Minkowski geometric flow in the plane

created by novaga on 15 Oct 2017

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Submitted Paper

Inserted: 15 oct 2017
Last Updated: 15 oct 2017

Year: 2017

Abstract:

We consider a planar geometric flow in which the normal velocity is a nonlocal variant of the curvature. The flow is not scaling invariant and in fact has diff erent behaviors at di fferent spatial scales, thus producing phenomena that are diff erent with respect to both the classical mean curvature flow and the fractional mean curvature flow. In particular, we give examples of neckpinch singularity formation, we show that sets with "sufficiently small interior" remain convex under the flow, but, on the other hand, in general the flow does not preserve convexity. We also take into account traveling waves for this geometric flow, showing that a new family of $C^2$ and convex traveling sets arises in this setting.