Simultaneous unitarizability of SL${}_{\mathit{\text{n}}}ℂ$-valued maps, and constant mean curvature $k$-noid monodromy
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 5 (2006) no. 4, p. 549-577

We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into ${\mathrm{SL}}_{n}ℂ$ 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 $k$-noids, genus-zero constant mean curvature surfaces with three or more ends in euclidean, spherical and hyperbolic $3$-spaces.

Classification:  53C42,  53A35,  49Q10
@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},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 5},
number = {4},
year = {2006},
pages = {549-577},
zbl = {1150.53021},
language = {en},
url = {http://www.numdam.org/item/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, Serie 5, Volume 5 (2006) no. 4, pp. 549-577. http://www.numdam.org/item/ASNSP_2006_5_5_4_549_0/

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