Cylindrical estimates for hypersurfaces moving by convex curvature functions

Abstract

We prove a complete family of `cylindrical estimates' for solutions of a class of fully non-linear curvature flows, generalising the cylindrical estimate of Huisken-Sinestrari for the mean curvature flow. More precisely, we show that, for the class of flows considered, an $(m+1)$-convex ($0\le m\le n-2$) solution becomes either strictly $m$-convex, or its Weingarten map approaches that of a cylinder ${\mathbb{R}}^m\times S^{n-m}$ at points where the curvature is becoming large. This result complements the convexity estimate proved by the authors and McCoy for the same class of flows.

Cited by in corpus (1)

• Cylindrical estimates for mean curvature flow of hypersurfaces in CROSSes