R^2$ 中的对数闵科夫斯基问题

Pub Date : 2024-04-03 DOI:10.4310/pamq.2024.v20.n2.a5

Yude Liu, Xinbao Lu, Qiang Sun, Ge Xiong

{"title":"R^2$ 中的对数闵科夫斯基问题","authors":"Yude Liu, Xinbao Lu, Qiang Sun, Ge Xiong","doi":"10.4310/pamq.2024.v20.n2.a5","DOIUrl":null,"url":null,"abstract":"A necessary condition for the existence of solutions to the logarithmic Minkowski problem in $\\mathbb{R}^2$, which turns to be stronger than the celebrated subspace concentration condition, is given. The sufficient and necessary conditions for the existence of solutions to the logarithmic problem for quadrilaterals, as well as the number of solutions, are fully characterized.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The logarithmic Minkowski problem in $R^2$\",\"authors\":\"Yude Liu, Xinbao Lu, Qiang Sun, Ge Xiong\",\"doi\":\"10.4310/pamq.2024.v20.n2.a5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A necessary condition for the existence of solutions to the logarithmic Minkowski problem in $\\\\mathbb{R}^2$, which turns to be stronger than the celebrated subspace concentration condition, is given. The sufficient and necessary conditions for the existence of solutions to the logarithmic problem for quadrilaterals, as well as the number of solutions, are fully characterized.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/pamq.2024.v20.n2.a5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/pamq.2024.v20.n2.a5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

给出了$\mathbb{R}^2$中对数闵科夫斯基问题解存在的必要条件，该条件比著名的子空间集中条件更强。充分描述了四边形对数问题解存在的充分条件和必要条件以及解的数量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

The logarithmic Minkowski problem in $R^2$

A necessary condition for the existence of solutions to the logarithmic Minkowski problem in $\mathbb{R}^2$, which turns to be stronger than the celebrated subspace concentration condition, is given. The sufficient and necessary conditions for the existence of solutions to the logarithmic problem for quadrilaterals, as well as the number of solutions, are fully characterized.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助