The Lp Chord Minkowski Problem for Negative p

被引：0
|
作者：
Li, Yuanyuan [1 ]
机构：
[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China
来源：
JOURNAL OF GEOMETRIC ANALYSIS | 2024年 / 34卷 / 03期
关键词：
Chord integral; <mml:msub>Lp</mml:msub> chord measure; <mml:msub>Lp</mml:msub> chord Minkowski problem; Monge- Ampere equation; 49J35; 35A15; FIREY THEORY; CURVATURE; CURVES;
D O I：
10.1007/s12220-023-01528-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we solve the Lp chord Minkowski problem in the case of discrete measures whose supports are in general position for p<0 and q>0. As for general Borel measure, we also give a proof but requiring -n<p<0 and n+1>q1. The Lp 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 Lp chord measure of a convex body. Moreover, The Lp chord Minkowski problem includes the chord Minkowski problem and the Lp Minkowski problem.
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页数：23
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