Pinching estimates of hypersurfaces by a generalized Gauss curvature flow

2023/11/30 by Hu, Jinrong, Zhang, Ping
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.18606

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\citeCW85 to the possible non-homogeneous curvature flows.

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