Finite type minimal annuli in S2 x R
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Date
2013
Authors
Hauswirth, L.
Kilian, Martin
Schmidt, M. U.
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Publisher
University of Illinois
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Abstract
We study minimal annuli in S2 × R of finite type by relating them to harmonic maps C → S2 of finite type. We rephrase an iteration by Pinkall–Sterling in terms of polynomial Killing fields. We discuss spectral curves, spectral data and the geometry of the isospectral set. We consider polynomial Killing fields with zeroes and the corresponding singular spectral curves, bubbletons and simple factors. We investigate the differentiable structure on the isospectral set of any finite type minimal annulus. We apply the theory to a 2-parameter family of embedded minimal annuli foliated by horizontal circles.
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Keywords
Pinkall–Sterling , Polynomial Killing fields , 2-parameter family of embedded minimal annuli foliated by horizontal circles
Citation
Hauswirth, L., Kilian, M. and Schmidt, M. U. (2013) 'Finite type minimal annuli in S2 x R', Illinois Journal of Mathematics, 57(3), pp. 697-741. doi: 10.1215/ijm/1415023507
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© 2013, University of Illinois.