A local estimate for the mean curvature flow

TL;DR

This paper derives a pointwise estimate for the second fundamental form during mean curvature flow, linking it to initial conditions and curvature bounds, leading to extension and blowup rate results.

Contribution

It introduces a new pointwise estimate for the second fundamental form in mean curvature flow based on initial geometry and curvature bounds.

Findings

Established a pointwise estimate of A during mean curvature flow.

Derived an extension theorem for the second fundamental form.

Provided a blowup rate estimate for the second fundamental form.

Abstract

We establish a pointwise estimate of A along the mean curvature flow in terms of the initial geometry and the jHAj bound. As corollaries we obtain the extension theorem of HA and the blowup rate estimate of HA.