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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Coarse classification of constant mean curvature cylinders
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by J. Dorfmeister and S.-P. Kobayashi PDF
Trans. Amer. Math. Soc. 359 (2007), 2483-2500 Request permission

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
  • 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.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 2483-2500
  • MSC (2000): Primary 53A10
  • DOI: https://doi.org/10.1090/S0002-9947-07-04063-9
  • MathSciNet review: 2286041