逆高斯曲率流与Orlicz Minkowski问题

Pub Date : 2022-01-01 DOI:10.1515/agms-2022-0146

Bin Chen, Jingshi Cui, P. Zhao

{"title":"逆高斯曲率流与Orlicz Minkowski问题","authors":"Bin Chen, Jingshi Cui, P. Zhao","doi":"10.1515/agms-2022-0146","DOIUrl":null,"url":null,"abstract":"Abstract Liu and Lu [27] investigated a generalized Gauss curvature flow and obtained an even solution to the dual Orlicz-Minkowski problem under some appropriate assumptions. The present paper investigates a inverse Gauss curvature flow, and achieves the long-time existence and convergence of this flow via a different C0-estimate technique under weaker conditions. As an application of this inverse Gauss curvature flow, the present paper first arrives at a non-even smooth solution to the Orlicz Minkowski problem.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Inverse Gauss Curvature Flows and Orlicz Minkowski Problem\",\"authors\":\"Bin Chen, Jingshi Cui, P. Zhao\",\"doi\":\"10.1515/agms-2022-0146\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Liu and Lu [27] investigated a generalized Gauss curvature flow and obtained an even solution to the dual Orlicz-Minkowski problem under some appropriate assumptions. The present paper investigates a inverse Gauss curvature flow, and achieves the long-time existence and convergence of this flow via a different C0-estimate technique under weaker conditions. As an application of this inverse Gauss curvature flow, the present paper first arrives at a non-even smooth solution to the Orlicz Minkowski problem.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/agms-2022-0146\",\"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/10.1515/agms-2022-0146","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

Liu和Lu研究了广义高斯曲率流，在适当的假设条件下得到了对偶Orlicz-Minkowski问题的偶解。本文研究了一种反高斯曲率流，在较弱的条件下，通过一种不同的c0估计技术，得到了该流的长时间存在性和收敛性。作为逆高斯曲率流的一个应用，本文首先得到了Orlicz Minkowski问题的非均匀光滑解。

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

Inverse Gauss Curvature Flows and Orlicz Minkowski Problem

Abstract Liu and Lu [27] investigated a generalized Gauss curvature flow and obtained an even solution to the dual Orlicz-Minkowski problem under some appropriate assumptions. The present paper investigates a inverse Gauss curvature flow, and achieves the long-time existence and convergence of this flow via a different C0-estimate technique under weaker conditions. As an application of this inverse Gauss curvature flow, the present paper first arrives at a non-even smooth solution to the Orlicz Minkowski problem.

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