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arXiv · 2001.07324

Flow by Gauss curvature to Dual Orlicz-Minkowski problems

Li Chen·Qiang Tu·Di Wu·Ni Xiang
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Abstract

In this paper we study a normalised anisotropic Gauss curvature flow of strictly convex, closed hypersurfaces in the Euclidean space R^n+1. We prove that the flow exists for all time and converges smoothly to the unique, strictly convex solution of a Monge-Amp`ere type equation. Our argument provides a parabolic proof in the smooth category for the existence of solutions to the Dual Orlicz-Minkowski problem introduced by Zhu, Xing and Ye.

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Li Chen, Qiang Tu, Di Wu, Ni Xiang. 2020-01-21. Flow by Gauss curvature to Dual Orlicz-Minkowski problems. https://arxiv.org/abs/2001.07324

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