{"title":"The Lp chord Minkowski problem","authors":"Dongmeng Xi, Deane Yang, Gaoyong Zhang, Yiming Zhao","doi":"10.1515/ans-2022-0041","DOIUrl":null,"url":null,"abstract":"Abstract Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n {{\\mathbb{R}}}^{n} , in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p {L}_{p} chord measures is called the L p {L}_{p} chord Minkowski problem in the L p {L}_{p} Brunn-Minkowski theory, which includes the L p {L}_{p} Minkowski problem as a special case. This article solves the L p {L}_{p} chord Minkowski problem when p > 1 p\\gt 1 and the symmetric case of 0 < p < 1 0\\lt p\\lt 1 .","PeriodicalId":7191,"journal":{"name":"Advanced Nonlinear Studies","volume":" ","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advanced Nonlinear Studies","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ans-2022-0041","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 8
Abstract
Abstract Chord measures are newly discovered translation-invariant geometric measures of convex bodies in R n {{\mathbb{R}}}^{n} , in addition to Aleksandrov-Fenchel-Jessen’s area measures. They are constructed from chord integrals of convex bodies and random lines. Prescribing the L p {L}_{p} chord measures is called the L p {L}_{p} chord Minkowski problem in the L p {L}_{p} Brunn-Minkowski theory, which includes the L p {L}_{p} Minkowski problem as a special case. This article solves the L p {L}_{p} chord Minkowski problem when p > 1 p\gt 1 and the symmetric case of 0 < p < 1 0\lt p\lt 1 .
弦测度是在R n {{\mathbb{R}}}^{n}中新发现的凸体的平移不变几何测度，是对aleksandrov - fenchell - jessen面积测度的补充。它们由凸体和随机线的弦积分构成。在L p {L} {p} Brunn-Minkowski理论中，规定L p {L} {p}弦测度称为L p {L} {p}弦Minkowski问题，其中包括L p {L} {p} Minkowski问题作为一个特例。本文解决了p bbb1p \gt 1时的L p {L}_{p}弦Minkowski问题以及0 < p < 1 0\lt p\lt 1的对称情况。
期刊介绍：
Advanced Nonlinear Studies is aimed at publishing papers on nonlinear problems, particulalry those involving Differential Equations, Dynamical Systems, and related areas. It will also publish novel and interesting applications of these areas to problems in engineering and the sciences. Papers submitted to this journal must contain original, timely, and significant results. Articles will generally, but not always, be published in the order when the final copies were received.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
