Harnack inequality for the negative power Gaussian curvature flow

TL;DR

This paper proves a Harnack inequality for the negative power Gaussian curvature flow of convex hypersurfaces, expanding understanding of curvature flow behavior under specific power conditions.

Contribution

It establishes a new Harnack inequality for the Gaussian curvature flow with negative powers, under particular restrictions related to the hypersurface's dimension.

Findings

Harnack inequality holds for negative powers of Gaussian curvature flow

The inequality requires the power's absolute value to be positive and less than the inverse of the hypersurface's dimension

Provides conditions under which the curvature flow exhibits certain regularity properties

Abstract

In this paper, we study the power of Gaussian curvature flow of a compact convex hypersurface and establish its Harnack inequality when the power is negative. In the Harnack inequality, we require that the absolute value of the power is strictly positive and strictly less than the inverse of the dimension of the hypersurface.