Lp扭转测度Minkowski问题解的连续性

Pub Date : 2023-01-01 DOI:10.2298/fil2308387l

Ni Li, Shuang Mou

{"title":"Lp扭转测度Minkowski问题解的连续性","authors":"Ni Li, Shuang Mou","doi":"10.2298/fil2308387l","DOIUrl":null,"url":null,"abstract":"This paper deals with on the continuity of the solution to the Minkowski problem for Lp torsional measure. For p ? (1, n + 2) ? (n + 2,?), we show that a sequence of convex bodies in Rn is convergent in Hausdorff metric if the sequence of the Lp torsional measures (associated with these convex bodies) is weakly convergent. Moreover, we also prove that the solution to the Minkowski problem for Lp torsional measure is continuous with respect to p.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the continuity of the solution to the Minkowski problem for Lp torsional measure\",\"authors\":\"Ni Li, Shuang Mou\",\"doi\":\"10.2298/fil2308387l\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with on the continuity of the solution to the Minkowski problem for Lp torsional measure. For p ? (1, n + 2) ? (n + 2,?), we show that a sequence of convex bodies in Rn is convergent in Hausdorff metric if the sequence of the Lp torsional measures (associated with these convex bodies) is weakly convergent. Moreover, we also prove that the solution to the Minkowski problem for Lp torsional measure is continuous with respect to p.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2298/fil2308387l\",\"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/10.2298/fil2308387l","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

本文讨论了Lp扭转测度Minkowski问题解的连续性问题。对于p ?(1, n + 2) ?(n + 2，?)，我们证明了如果(与这些凸体相关的)Lp扭转测度序列弱收敛，则Rn中的凸体序列在Hausdorff度量中收敛。此外，我们还证明了Lp扭转测度Minkowski问题的解相对于p是连续的。

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

微信好友朋友圈 QQ好友复制链接

On the continuity of the solution to the Minkowski problem for Lp torsional measure

This paper deals with on the continuity of the solution to the Minkowski problem for Lp torsional measure. For p ? (1, n + 2) ? (n + 2,?), we show that a sequence of convex bodies in Rn is convergent in Hausdorff metric if the sequence of the Lp torsional measures (associated with these convex bodies) is weakly convergent. Moreover, we also prove that the solution to the Minkowski problem for Lp torsional measure is continuous with respect to p.

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