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Unitarization of monodromy representations and constant mean curvature trinoids in 3‐dimensional space forms
Author(s) -
Schmitt N.,
Kilian M.,
Kobayashi S.-P.,
Rossman W.
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm005
Subject(s) - monodromy , mathematics , constant curvature , constant (computer programming) , space (punctuation) , pure mathematics , curvature , simply connected space , mean curvature , space frame , group (periodic table) , mathematical analysis , geometry , physics , computer science , quantum mechanics , programming language , thermodynamics , operating system
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 ℝ 3 , 3 and ℍ 3 . Additionally, the extended frame for any associated family of Delaunay surfaces is computed.