Local convexity estimates for mean curvature flow

TL;DR

This paper introduces a local version of Huisken-Stampacchia iteration to derive sharp curvature pinching estimates for mean curvature flow, independent of noncollapsing conditions, applicable in various settings.

Contribution

It develops a novel local iteration method that yields curvature estimates without relying on noncollapsing assumptions, broadening applicability.

Findings

Established local curvature pinching estimates for mean curvature flow.

Method applicable to diverse geometric evolution problems.

Does not depend on noncollapsing conditions.

Abstract

We develop a local version of Huisken-Stampacchia iteration, using it to obtain local versions of a host of important sharp curvature pinching estimates for mean curvature flow. The local estimates we obtain do not depend on the quality of noncollapsing of the solution and the method adopted applies in a host of other settings.