Regularity and stability results for the level set flow via the mean curvature flow with surgery

TL;DR

This paper uses mean curvature flow with surgery to establish regularity and stability results for the level set flow, especially in 2-convex regions, extending beyond Brakke regularity.

Contribution

It introduces new regularity estimates for the level set flow using surgery techniques and proves a stability result for the plane under this flow.

Findings

Regularity estimates for level set flow beyond Brakke regularity.

Stability of the plane under level set flow.

Application to 2-convex regions of high density.

Abstract

In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowing for 2-convex regions of high density. We also show a stability result for the plane under the level set flow.