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

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.

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Received 15 February 2018

Accepted 4 March 2019

Published 24 May 2022