A class of anisotropic inverse Gauss curvature flows and dual Orlicz Minkowski type problem

2022/09/10 by Shanwei Ding, Ding, Shanwei, Guanghan Li +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2209.04601

openalex publication_date 2022/09/10 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the long-time existence and asymptotic behavior for a class of anisotropic inverse Gauss curvature flows. By the stationary solutions of anisotropic flows, we obtain some new existence results for the dual Orlicz Minkowski type problem and even dual Orlicz Minkowski type problem for smooth measures, which is the most reasonable extension of the L^p dual Minkowski problem from the dual point of view. The results of corresponding L^p versions are L^p dual Minkowski problem for p>q; and even L^p dual Minkowski problem for p>-1, or q<1, or some ranges of p<0

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