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Journal of the London Mathematical Society Advance Access originally published online on June 4, 2007
Journal of the London Mathematical Society 2007 75(3):563-581; doi:10.1112/jlms/jdm005
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© 2007 London Mathematical Society

Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms

N. Schmitt1, M. Kilian2,, S.-P. Kobayashi3 and W. Rossman4

1 Institut für Mathematik
Technische Universität Berlin
10623 Berlin
Germany
2 Mathematical Sciences
University of Bath
Bath, BA2 7AY
United Kingdom
3 School of Information Environment
Tokyo Denki University
Chiba 270-1382
Japan
4 Department of Mathematics
Kobe University
Rokko Kobe 657-8501
Japan

A theorem on the unitarizability of loop group valued monodromy representations is presented and applied to show the existence of new families of constant mean curvature surfaces homeomorphic to a thrice-punctured sphere in the simply connected 3-dimensional space forms R3, S3 and H3. Additionally, the extended frame for any associated family of Delaunay surfaces is computed.

kilian{at}rumms.uni-mannheim.de

2000 Mathematics Subject Classification 53A10.

The first author was supported by National Science Foundation grant DMS-00-76085. The second author was supported by EPSRC grant GR/S28655/01. The third and fourth authors were supported by Japan Monbusho grants C-2 11640070 and B-1 15340023.

Received June 9, 2005; revised May 10, 2006; published online June 4, 2007.


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