Harnack inequality for the negative power Gaussian curvature flow

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 absolutevalue of the power is strictly positive and strictly less than the inverse of the dimension of the hypersurface. © 2011 American Mathematical Society.