On Brendle’s Estimate for the Inscribed Radius Under Mean Curvature Flow

Abstract

In a recent paper [3], Brendle proved that the inscribed radius of closed embedded mean convex hypersurfaces moving by mean curvature flow is at least |$\frac {1}{(1+\delta)H}$| at all points with H≥C(δ,M0). In this note, we give a shorter proof of Brendle’s estimate, and of a more general result for α-Andrews flows, based on our recent estimates from Haslhofer and Kleiner [4].