The L_p Minkowski problems on affine dual quermassintegrals

2025/04/16 by Youjiang Lin, Lin, Youjiang, Yuchi Wu +1 · 1 citation
Mathematics · #52A20 #52A30 #52A40 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2504.12117

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we extend the affine dual curvature measures to the L_p setting and solve the existence part of the corresponding Minkowski problem for non-symmetric discrete measures when p>1 and for symmetric measures when p≥0. When p=0, the L₀ Minkowski problem is the affine dual Minkowski problem, which is introduced and solved by Cai-Leng-Wu-Xi in [6].

Cited by

• Anisotropic fractional area measures

Related

• The Minkowski problem based on the (p,q)-mixed quermassintegrals
• The L_p dual Minkowski problem for p>1 and q>0
• Uniqueness and continuity of the solution to L_p dual Minkowski problem
• The mixed affine quermassintegrals
• The dual Orlicz-Minkowski problem