Deforming a convex hypersurface with low entropy by its Gauss curvature

TL;DR

This paper demonstrates that convex hypersurfaces with initially low entropy become asymptotically round when evolved under normalized Gauss curvature flow.

Contribution

It establishes a new result linking low initial entropy to the asymptotic roundness of convex hypersurfaces under Gauss curvature flow.

Findings

Convex hypersurfaces with small initial entropy become round over time.

Normalized Gauss curvature flow leads to asymptotic roundness under certain conditions.

The entropy condition is crucial for the convergence result.

Abstract

We prove the asymptotic roundness under normalized Gauss curvature flow provided entropy is initially small enough.