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A strong Frankel Theorem for shrinkers

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arxiv 2306.08078 v1 pith:HPAYGXNH submitted 2023-06-13 math.DG

Tobias Holck Colding , William P. Minicozzi II This is my paper · ORCID
classification math.DG
keywords shrinkersstrongtheoremfrankellargemustballballs
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We prove a strong Frankel theorem for mean curvature flow shrinkers in all dimensions: Any two shrinkers in a sufficiently large ball must intersect. In particular, the shrinker itself must be connected in all large balls. The key to the proof is a strong Bernstein theorem for incomplete stable Gaussian surfaces.

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  1. Singularities of mean curvature flow with bounded mean curvature and Morse index

    math.DG 2025-01 conditional novelty 8.0 of 10

    For closed smooth mean curvature flows in R^{n+1}, 3≤n≤6, at the first singular time either the mean curvature or the Morse index must blow up.

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