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Deforming a Convex Hypersurface by Anisotropic Curvature Flows
Advanced Nonlinear Studies ( IF 1.8 ) Pub Date : 2020-10-02 , DOI: 10.1515/ans-2020-2108
HongJie Ju 1 , BoYa Li 2 , YanNan Liu 2
Affiliation  

In this paper, we consider a fully nonlinear curvature flow of a convex hypersurface in the Euclidean n-space. This flow involves k-th elementary symmetric function for principal curvature radii and a function of support function. Under some appropriate assumptions, we prove the long-time existence and convergence of this flow. As an application, we give the existence of smooth solutions to the Orlicz-Christoffel-Minkowski problem.

中文翻译:

通过各向异性曲率流变形凸超曲面

在本文中,我们考虑欧几里得 n 空间中凸超曲面的完全非线性曲率流。该流程涉及主曲率半径的第 k 个初等对称函数和支持函数的函数。在一些适当的假设下,我们证明了这个流的长期存在和收敛。作为一个应用,我们给出了 Orlicz-Christoffel-Minkowski 问题的光滑解的存在性。
更新日期:2020-10-02
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