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.
Revisiting generic mean curvature flow inR 3.arXiv preprint arXiv:2409.01463
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Any smooth closed immersed curve in R^n with a one-to-one convex projection onto a 2-plane develops a Type I singularity and becomes asymptotically circular under curve shortening flow, enabling a perturbation result that is an analog of Huisken's conjecture.
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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.
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Singularities of Curve Shortening Flow with Convex Projections
Any smooth closed immersed curve in R^n with a one-to-one convex projection onto a 2-plane develops a Type I singularity and becomes asymptotically circular under curve shortening flow, enabling a perturbation result that is an analog of Huisken's conjecture.