旋转域中的间隙结果和自由边界 CMC 表面的存在

IF 1.3 2区数学 Q1 MATHEMATICS Nonlinear Analysis-Theory Methods & Applications Pub Date : 2024-10-30 DOI:10.1016/j.na.2024.113681

{"title":"旋转域中的间隙结果和自由边界 CMC 表面的存在","authors":"","doi":"10.1016/j.na.2024.113681","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we work with the existence and uniqueness of free boundary constant mean curvature surfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. We classify the free boundary CMC surfaces as topological disks or annulus under some conditions on the function that generates the graph and a gap condition on the umbilicity tensor. Also, we construct some examples of free boundary CMC surfaces in the rotational ellipsoid that, in particular, satisfy our gap condition.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Gap results and existence of free boundary CMC surfaces in rotational domains\",\"authors\":\"\",\"doi\":\"10.1016/j.na.2024.113681\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we work with the existence and uniqueness of free boundary constant mean curvature surfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. We classify the free boundary CMC surfaces as topological disks or annulus under some conditions on the function that generates the graph and a gap condition on the umbilicity tensor. Also, we construct some examples of free boundary CMC surfaces in the rotational ellipsoid that, in particular, satisfy our gap condition.</div></div>\",\"PeriodicalId\":49749,\"journal\":{\"name\":\"Nonlinear Analysis-Theory Methods & Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Theory Methods & Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0362546X24002001\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Theory Methods & Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0362546X24002001","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: 0

摘要

本文研究旋转域中自由边界恒均值曲率曲面的存在性和唯一性。这些域的边界由图形的旋转产生。根据生成图形的函数的一些条件和脐张量的间隙条件，我们将自由边界 CMC 曲面归类为拓扑盘或环面。此外，我们还构建了一些旋转椭球体中的自由边界 CMC 曲面实例，这些曲面尤其满足我们的间隙条件。

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

本刊更多论文

Gap results and existence of free boundary CMC surfaces in rotational domains

In this paper, we work with the existence and uniqueness of free boundary constant mean curvature surfaces in rotational domains. These are domains whose boundary is generated by a rotation of a graph. We classify the free boundary CMC surfaces as topological disks or annulus under some conditions on the function that generates the graph and a gap condition on the umbilicity tensor. Also, we construct some examples of free boundary CMC surfaces in the rotational ellipsoid that, in particular, satisfy our gap condition.

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

来源期刊

Nonlinear Analysis-Theory Methods & Applications 数学-数学

CiteScore

3.30

自引率

0.00%

发文量

265

审稿时长

60 days

期刊介绍： Nonlinear Analysis focuses on papers that address significant problems in Nonlinear Analysis that have a sustainable and important impact on the development of new directions in the theory as well as potential applications. Review articles on important topics in Nonlinear Analysis are welcome as well. In particular, only papers within the areas of specialization of the Editorial Board Members will be considered. Authors are encouraged to check the areas of expertise of the Editorial Board in order to decide whether or not their papers are appropriate for this journal. The journal aims to apply very high standards in accepting papers for publication.