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Coarse classification of constant mean curvature cylinders


Authors: J. Dorfmeister and S.-P. Kobayashi
Journal: Trans. Amer. Math. Soc. 359 (2007), 2483-2500
MSC (2000): Primary 53A10
DOI: https://doi.org/10.1090/S0002-9947-07-04063-9
Published electronically: January 4, 2007
MathSciNet review: 2286041
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Abstract: We give a coarse classification of constant mean curvature (CMC) immersions of cylinders into $ \mathbb{R}^3$ via the loop group method. Particularly for this purpose, we consider double loop groups and a new type of ``potentials'' which are meromorphic 1-forms on Riemann surfaces.


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Additional Information

J. Dorfmeister
Affiliation: Zentrum Mathematik, Technische Universität München Boltzmannstr. 3, D-85747, Garching, Germany
Email: dorfm@ma.tum.de

S.-P. Kobayashi
Affiliation: School of Information Environment, Tokyo Denki University Muzai Gakuendai 2-1200 Inzai, Chiba 270-1382, Japan
Email: shimpei@sie.dendai.ac.jp

DOI: https://doi.org/10.1090/S0002-9947-07-04063-9
Keywords: Constant mean curvature surfaces, loop groups
Received by editor(s): December 7, 2004
Published electronically: January 4, 2007
Additional Notes: The first author acknowledges support by DFG
The second author was fully supported by DFG grant DO776/1.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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