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

Joshua Daniels-Holgate

Published 2021-04-23Version 1

We construct smooth mean curvature flows with surgery that approximate unit-regular, cylic (mod 2) Brakke 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.