On Brendle's estimate for the inscribed radius under mean curvature flow

TL;DR

This paper provides a shorter proof of Brendle's estimate on the inscribed radius under mean curvature flow, extending it to alpha-Andrews flows using recent estimates, thereby simplifying and generalizing previous results.

Contribution

The authors present a more concise proof of Brendle's estimate and extend it to alpha-Andrews flows, leveraging recent advances from Haslhofer-Kleiner.

Findings

Shorter proof of Brendle's estimate established

Extension of the estimate to alpha-Andrews flows demonstrated

Based on recent estimates, the results are more general and simplified

Abstract

In a recent paper, Brendle proved that the inscribed radius of closed embedded mean convex hypersurfaces moving by mean curvature flow is at least 1/((1+\delta)H) at all points with H > C(\delta,M_0). In this note, we give a shorter proof of Brendle's estimate, and of a more general result for alpha-Andrews flows, based on our recent estimates from Haslhofer-Kleiner.