Free Boundary Minimal Annuli Immersed in the Unit Ball

IF 2.6 1区 数学 Q1 MATHEMATICS, APPLIED
Isabel Fernández, Laurent Hauswirth, Pablo Mira
{"title":"Free Boundary Minimal Annuli Immersed in the Unit Ball","authors":"Isabel Fernández,&nbsp;Laurent Hauswirth,&nbsp;Pablo Mira","doi":"10.1007/s00205-023-01943-z","DOIUrl":null,"url":null,"abstract":"<div><p>We construct a family of compact free boundary minimal annuli immersed in the unit ball <span>\\(\\mathbb {B}^3\\)</span> of <span>\\(\\mathbb {R}^3\\)</span>, the first such examples other than the critical catenoid. This solves a problem formulated by Nitsche in 1985. These annuli are symmetric with respect to two orthogonal planes and a finite group of rotations around an axis, and are foliated by spherical curvature lines. We show that the only free boundary minimal annulus embedded in <span>\\(\\mathbb {B}^3\\)</span> foliated by spherical curvature lines is the critical catenoid; in particular, the minimal annuli that we construct are not embedded. On the other hand, we also construct families of non-rotational compact embedded capillary minimal annuli in <span>\\(\\mathbb {B}^3\\)</span>. Their existence solves in the negative a problem proposed by Wente in 1995.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":"247 6","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00205-023-01943-z.pdf","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Rational Mechanics and Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-023-01943-z","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 8

Abstract

We construct a family of compact free boundary minimal annuli immersed in the unit ball \(\mathbb {B}^3\) of \(\mathbb {R}^3\), the first such examples other than the critical catenoid. This solves a problem formulated by Nitsche in 1985. These annuli are symmetric with respect to two orthogonal planes and a finite group of rotations around an axis, and are foliated by spherical curvature lines. We show that the only free boundary minimal annulus embedded in \(\mathbb {B}^3\) foliated by spherical curvature lines is the critical catenoid; in particular, the minimal annuli that we construct are not embedded. On the other hand, we also construct families of non-rotational compact embedded capillary minimal annuli in \(\mathbb {B}^3\). Their existence solves in the negative a problem proposed by Wente in 1995.

Abstract Image

自由边界最小环空浸入单位球
在\(\mathbb {R}^3\)的单位球\(\mathbb {B}^3\)中构造了一个紧致自由边界极小环空族,这是除临界链面外的第一个此类例子。这解决了尼采在1985年提出的一个问题。这些环空相对于两个正交平面和围绕一个轴的有限组旋转是对称的,并且由球面曲率线分叶。我们证明了由球面曲率线片理的\(\mathbb {B}^3\)中嵌入的唯一自由边界最小环是临界链状体;特别是,我们构建的最小环空没有嵌入。另一方面,我们也在\(\mathbb {B}^3\)中构造了非旋转致密嵌入毛细管最小环空族。它们的存在从反面解决了文特在1995年提出的一个问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
5.10
自引率
8.00%
发文量
98
审稿时长
4-8 weeks
期刊介绍: The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信