On an extention of the H^k mean curvature flow of closed convex hypersurfaces

TL;DR

This paper proves that the H^k mean curvature flow of closed convex hypersurfaces can be extended beyond maximal time if the total L^p integral of the mean curvature remains finite, for odd k > 2.

Contribution

It extends previous results by establishing conditions under which the H^k mean curvature flow can be continued, specifically for odd k greater than 2.

Findings

Flow can be extended if the L^p integral of mean curvature is finite.

Applicable to convex hypersurfaces in higher dimensions.

Provides new criteria for flow continuation.

Abstract

In this paper we prove that the H^k (k is odd and larger than 2) mean curvature flow of a closed convex hypersurface can be extended over the maximal time provided that the total L^p integral of the mean curvature is finite for some p