Properly embedded minimal annuli in S2 x R

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dc.contributor.authorHauswirth, L.
dc.contributor.authorKilian, Martin
dc.contributor.authorSchmidt, M. U.
dc.date.accessioned2023-10-10T10:40:23Z
dc.date.available2023-10-04T13:57:06Zen
dc.date.available2023-10-10T10:40:23Z
dc.date.issued2020-09-23
dc.date.updated2023-10-04T12:57:10Zen
dc.description.abstractWe prove that every properly embedded minimal annulus in S2 × R is foliated by circles. We show that such minimal annuli are given by periodic harmonic maps C → S2 of finite type. Such harmonic maps are parameterized by spectral data, and we show that continuous deformations of the spectral data preserve the embeddedness of the corresponding annuli. A curvature estimate of Meeks and Rosenberg is used to show that each connected component of spectral data of embedded minimal annuli contains a maximum of the flux of the third coordinate. A classification of these maxima allows us to identify the spectral data of properly embedded minimal annuli with the spectral data of minimal annuli foliated by circles.
dc.description.statusPeer revieweden
dc.description.versionPublished Version
dc.format.mimetypeapplication/pdfen
dc.identifier.articleidxyaa005
dc.identifier.citationHauswirth, L., Kilian, M. and Schmidt, M. U. (2020) 'Properly embedded minimal annuli in S2×R', Journal of Integrable Systems, 5(1), xyaa005 (37pp). doi: 10.1093/integr/xyaa005
dc.identifier.doi10.1093/integr/xyaa005
dc.identifier.eissn2058-5985
dc.identifier.endpage37
dc.identifier.issued1
dc.identifier.journaltitleJournal of Integrable Systems
dc.identifier.startpage1
dc.identifier.urihttps://hdl.handle.net/10468/15091
dc.identifier.volume5
dc.language.isoenen
dc.publisherOxford University Press
dc.rights© 2020, the Authors. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectMinimal surface
dc.subjectHarmonic map
dc.subjectSpectral curve
dc.titleProperly embedded minimal annuli in S2 x Ren
dc.typeArticle (peer-reviewed)
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