Universality in mean curvature flow neckpinches
classification
🧮 math.DG
math.AP
keywords
flowwillcurvaturemeantimeassumptionsasymptoticallybecome
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We study noncompact surfaces evolving by mean curvature flow. Without any symmetry assumptions, we prove that any solution that is $C^3$-close at some time to a standard neck will develop a neckpinch singularity in finite time, will become asymptotically rotationally symmetric in a space-time neighborhood of its singular set, and will have a unique tangent flow.
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