Neckpinch Singularities in Fractional Mean Curvature Flows
نویسندگان
چکیده
In this paper we consider the evolution of sets by a fractional mean curvature flow. Our main result states that for any dimension n > 2, there exists an embedded surface in R evolving by fractional mean curvature flow, which developes a singularity before it can shrink to a point. When n > 3 this result generalizes the analogue result of Grayson [18] for the classical mean curvature flow. Interestingly, when n = 2, our result provides instead a counterexample in the nonlocal framework to the well known Grayson Theorem [19], which states that any smooth embedded curve in the plane evolving by (classical) MCF shrinks to a point.
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