Regularity of the p-Gauss Curvature Flow with Flat Sides

Abstract

The authors study the regularity of the p-Gauss curvature flow with flat sides. In their previous paper [Huang, G. G., Wang, X.-J. and Zhou, Y., Long time regularity of the p-Gauss curvature flow with flat side, https://arxiv.org/abs/2403.12292], they obtained the regularity of the interface, namely the boundary of the flat part. In this paper, they study the regularity of the convex hypersurface near the interface.

Keywords

Gauss curvature flow / Parabolic Monge-Ampère equation / Interface / Regularity

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