Properly embedded minimal annuli in S2 x R
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Published Version
Date
2020-09-23
Authors
Hauswirth, L.
Kilian, Martin
Schmidt, M. U.
Journal Title
Journal ISSN
Volume Title
Publisher
Oxford University Press
Published Version
Abstract
We 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.
Description
Keywords
Minimal surface , Harmonic map , Spectral curve
Citation
Hauswirth, 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