Nonparametric hypersurfaces moving by powers of Gauss curvature

TL;DR

This paper investigates the long-term behavior of nonparametric hypersurfaces evolving under a curvature-driven flow, specifically powers of Gauss curvature with exponents greater than 1/n, extending previous work for the case when the exponent is 1.

Contribution

It generalizes existing results on hypersurface evolution by Gauss curvature to a broader class involving powers greater than 1/n, providing new insights into their asymptotic behavior.

Findings

Extended the analysis of hypersurface evolution to powers of Gauss curvature greater than 1/n.

Provided asymptotic descriptions for the long-term behavior of these hypersurfaces.

Generalized prior results by V. Oliker for the case when the power is 1.

Abstract

We study asymptotic behavior of nonparametric hypersurfaces moving by $\alpha$ powers of Gauss curvature $\alpha > 1/n$. Our work generalizes the results of V. Oliker [Oli91] for $\alpha= 1$.