{"title":"Free Boundary Minimal Annuli Immersed in the Unit Ball","authors":"Isabel Fernández, Laurent Hauswirth, 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.
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.