{"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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"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":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00205-023-01943-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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.
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