The Lp chord Minkowski problem for negative p

2023/04/22 by Yuanyuan Li, Li, Yuanyuan
Computer Science · Mathematics · #35A15 #49J35 #Analysis of PDEs (math.AP) #F.2.2 #FOS: Mathematics #G.1.8 #Geochemistry and Geologic Mapping #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2304.11299

openalex publication_date 2023/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we solve the L_p chord Minkowski problem in the case of discrete measures whose supports are in general position for negative p and q>0. As for general Borel measure with a density, we also give a proof but need p∈(-n,0) and n+1>q\geqslant 1. The L_p chord Minkowski problem was recently posed by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the L_p chord measure of a convex body, and it includes the chord Minkowski problem and the L_p Minkowski problem.

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