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Differential Geometry

arXiv:dg-ga/9603007 (dg-ga)
[Submitted on 14 Mar 1996 (v1), last revised 19 Mar 1996 (this version, v2)]

Title:On symmetries of constant mean curvature surfaces

Authors:Josef Dorfmeister (Univ. of Kansas), Guido Haak (TU-Berlin)
View a PDF of the paper titled On symmetries of constant mean curvature surfaces, by Josef Dorfmeister (Univ. of Kansas) and 1 other authors
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Abstract: We start the investigation of immersions $\Psi$ of a simply connected domain $D$ into three dimensional Euclidean space $R^3$, which have constant mean curvature (CMC-immersions), and allow for a group of automorphisms of $D$ which leave the image $\Psi(D)$ invariant. On one hand, this leads to a detailed description of symmetric CMC-surfaces and the associated symmetry groups. On the other hand, it allows us to start the classification of CMC-immersions of an arbitrary, compact or noncompact Riemann surface $M$ into $R^3$ in terms of Weierstrass-type data, as introduced by Pedit, Wu, and one of the authors [D]. We use our general results to prove, that there are no CMC-tori or Delaunay surfaces in the dressing orbit of the cylinder. As an example, we apply the discussion to Smyth surfaces and to a CMC-surface with a branchpoint.
Comments: 42 pages, LaTeX, no figures, revision correcting several misprints
Subjects: Differential Geometry (math.DG)
Report number: SFB 288 Preprint No. 197 (TU-Berlin)
Cite as: arXiv:dg-ga/9603007
  (or arXiv:dg-ga/9603007v2 for this version)
  https://doi.org/10.48550/arXiv.dg-ga/9603007
arXiv-issued DOI via DataCite

Submission history

From: Guido Haak [view email]
[v1] Thu, 14 Mar 1996 09:24:32 UTC (42 KB)
[v2] Tue, 19 Mar 1996 14:31:48 UTC (42 KB)
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