Coarse classification of constant mean curvature cylinders

Dorfmeister, J.; Kobayashi, S.-P.

doi:10.1090/S0002-9947-07-04063-9

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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