Universality in mean curvature flow neckpinches

Abstract

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.

More references added, typos corrected

References in corpus (1)

• Formal matched asymptotics for degenerate Ricci flow neckpinches

Cited by in corpus (4)

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• A generic framework of adiabatic approximation for nonlinear evolutions II
• Adiabatic theory for the area-constrained Willmore flow