Simultaneous unitarizability of SL n ℂ -valued maps, and constant mean curvature k-noid monodromy

Wayne Rossman; Nicholas Schmitt

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2006)

  • Volume: 5, Issue: 4, page 549-577
  • ISSN: 0391-173X

Abstract

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We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into 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.

How to cite

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Rossman, Wayne, and 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 5.4 (2006): 549-577. <http://eudml.org/doc/242690>.

@article{Rossman2006,
abstract = {We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into $\{\rm SL\}_\{n\}\{\mathbb \{C\}\}$ 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.},
author = {Rossman, Wayne, Schmitt, Nicholas},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {549-577},
publisher = {Scuola Normale Superiore, Pisa},
title = {Simultaneous unitarizability of SL$_\{\hbox\{\textit \{n\}\}\}\{\mathbb \{C\}\}$-valued maps, and constant mean curvature k-noid monodromy},
url = {http://eudml.org/doc/242690},
volume = {5},
year = {2006},
}

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
PB - Scuola Normale Superiore, Pisa
VL - 5
IS - 4
SP - 549
EP - 577
AB - We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into ${\rm SL}_{n}{\mathbb {C}}$ 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.
LA - eng
UR - http://eudml.org/doc/242690
ER -

References

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