Constructs mean curvature flow with surgery for compact mean convex hypersurfaces in R^{n+1} by performing topological surgeries via nondegenerate cylindrical singularities with finite smooth-time adjustments.
Nondegenerate neck pinches along the mean curvature flow
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abstract
We show that for generic smooth compact initial surfaces the mean curvature flow in $\mathbb{R}^3$ has spherical or nondegenerate neck pinch singularities at the first singular time. In particular the singularities at the first singular time are isolated in spacetime. As an application we give a new approach to constructing a mean curvature flow with surgery for smooth compact initial surfaces in $\mathbb{R}^3$.
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math.DG 1years
2026 1verdicts
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Mean convex flows with surgery
Constructs mean curvature flow with surgery for compact mean convex hypersurfaces in R^{n+1} by performing topological surgeries via nondegenerate cylindrical singularities with finite smooth-time adjustments.