Approximation of mean curvature flow with generic singularities by smooth flows with surgery
Abstract
We construct smooth 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 demonstrate an application of this surgery flow by improving the entropy bound on the low-entropy Schoenflies conjecture.