We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into under conjugation by a single analytic matrix map.We apply this result to the monodromy arising from an integrable partial differential equation to construct a family of -noids, genus-zero constant mean curvature surfaces with three or more ends in euclidean, spherical and hyperbolic -spaces.
@article{ASNSP_2006_5_5_4_549_0, author = {Rossman, Wayne and Schmitt, Nicholas}, title = {Simultaneous unitarizability of {SL}$_{\hbox{\textit {n}}}{\mathbb {C}}$-valued maps, and constant mean curvature $k$-noid monodromy}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {549--577}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 5}, number = {4}, year = {2006}, zbl = {1150.53021}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2006_5_5_4_549_0/} }
TY - JOUR AU - Rossman, Wayne AU - Schmitt, Nicholas TI - Simultaneous unitarizability of SL$_{\hbox{\textit {n}}}{\mathbb {C}}$-valued maps, and constant mean curvature $k$-noid monodromy JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2006 SP - 549 EP - 577 VL - 5 IS - 4 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2006_5_5_4_549_0/ LA - en ID - ASNSP_2006_5_5_4_549_0 ER -
%0 Journal Article %A Rossman, Wayne %A Schmitt, Nicholas %T Simultaneous unitarizability of SL$_{\hbox{\textit {n}}}{\mathbb {C}}$-valued maps, and constant mean curvature $k$-noid monodromy %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2006 %P 549-577 %V 5 %N 4 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2006_5_5_4_549_0/ %G en %F ASNSP_2006_5_5_4_549_0
Rossman, Wayne; Schmitt, Nicholas. Simultaneous unitarizability of SL$_{\hbox{\textit {n}}}{\mathbb {C}}$-valued maps, and constant mean curvature $k$-noid monodromy. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 5 (2006) no. 4, pp. 549-577. http://www.numdam.org/item/ASNSP_2006_5_5_4_549_0/
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