A note on the Gauss curvature flow

TL;DR

This paper establishes a uniform lower bound on the Gauss curvature for solutions to the Gauss curvature flow by employing polar convex bodies and $C_0$-bounds, avoiding the use of Chow's Harnack inequality.

Contribution

It introduces a novel approach using polar convex bodies and $C_0$-bounds to analyze the Gauss curvature flow without relying on Chow's Harnack inequality.

Findings

Established a uniform lower bound on Gauss curvature

Applied polar convex bodies and $C_0$-bounds in the analysis

Provided an alternative method to previous curvature estimates

Abstract

Using polar convex bodies and the $C_0$-bounds from Guan and Ni \cite{PL}, we obtain a uniform lower bound on the Gauss curvature of the normalized solution of the Gauss curvature flow without using Chow's Harnack inequality \cite{Ch2}.