Pinching estimates of hypersurfaces by a generalized Gauss curvature flow
Analysis of PDEs
2023-12-01 v1
Abstract
A variant of the Gauss curvature flow for closed and convex hypersurfaces is considered. We reveal that if the initial hypersurface is pinched enough, then this property is preserved. Furthermore, based on some structure assumptions on the speed function of the shrinking flow, we show that the flow converges to a sphere. This may generalize the result of B. Chow\cite{CW85} to the possible non-homogeneous curvature flows.
Cite
@article{arxiv.2311.18606,
title = {Pinching estimates of hypersurfaces by a generalized Gauss curvature flow},
author = {Jinrong Hu and Ping Zhang},
journal= {arXiv preprint arXiv:2311.18606},
year = {2023}
}
Comments
This article was written in 2022 and still under review, we forgot to post it on arxiv