The horospherical p-Christoffel-Minkowski and prescribed p-shifted Weingarten curvature problems in hyperbolic space

2024/11/26 by Yingxiang Hu, Haizhong Li, Hu, Yingxiang +3
Engineering · Mathematics · #52A55 #58J05 #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2411.17345

openalex publication_date 2024/11/26 · openalex created_date 2024/12/05 · openalex updated_date 2026/07/28

Abstract

The L_p-Christoffel-Minkowski problem and the prescribed L_p-Weingarten curvature problem for convex hypersurfaces in Euclidean space are important problems in geometric analysis. In this paper, we consider their counterparts in hyperbolic space. For the horospherical p-Christoffel-Minkowski problem first introduced and studied by the second and third authors, we prove the existence of smooth, origin-symmetric, strictly horospherically convex solutions by establishing a new full rank theorem. We also propose the prescribed p-shifted Weingarten curvature problem and prove an existence result.

Related

• Smooth solutions to the Christoffel problem in ℍⁿ⁺¹
• The discrete horospherical p-Minkowski problem in hyperbolic space
• Non-normalized solutions to the horospherical Minkowski problem
• Hyperbolic p-sum and Horospherical p-Brunn-Minkowski theory in hyperbolic space
• Classification of solutions to the isotropic horospherical p-Minkowski problem in hyperbolic plane