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},
year = {2006},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 5},
number = {4},
zbl = {1150.53021},
language = {en},
url = {https://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 - https://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 https://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. https://www.numdam.org/item/ASNSP_2006_5_5_4_549_0/
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