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arXiv · 2104.11647

Approximation of mean curvature flow with generic singularities by smooth flows with surgery

Joshua Daniels-Holgate
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Abstract

We construct smooth mean curvature flows with surgery that approximate weak mean curvature flows with only spherical and neck-pinch singularities. This is achieved by combining the recent work of Choi-Haslhofer-Hershkovits, and Choi-Haslhofer-Hershkovits-White, establishing canonical neighbourhoods of such singularities, with suitable barriers to flows with surgery. A limiting argument is then used to control these approximating flows. We conclude by improving the entropy bound on the low-entropy Schoenflies conjecture.

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Joshua Daniels-Holgate. 2021-04-23. Approximation of mean curvature flow with generic singularities by smooth flows with surgery. https://doi.org/10.1016/j.aim.2022.108715

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