The L_p Chord Minkowski problem in a critical interval

2023/01/18 by Lujun Guo, Guo, Lujun, Dongmeng Xi +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Morphological variations and asymmetry #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2301.07603

openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Chord measures and L_p chord measures were recently introduced by Lutwak-Xi-Yang-Zhang by establishing a variational formula regarding a family of fundamental integral geometric invariants called chord integrals. Prescribing the L_p chord measure is known as the L_p chord Minkowski problem, which includes the L_p Minkowski problem heavily studied in the past 2 decades as special cases. In the current work, we solve the L_p chord Minkowski problem when 0≤ p<1, without symmetry assumptions.

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