Resumé
It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Monatshefte fur Mathematik |
| Vol/bind | 190 |
| Udgave nummer | 4 |
| Sider (fra-til) | 599-614 |
| Antal sider | 16 |
| ISSN | 0026-9255 |
| DOI | |
| Status | E-pub ahead of print - 28. jan. 2019 |
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Continuous deformations of harmonic maps and their unitons. / Aleman, Alexandru; Martín, María J.; Persson, Anna Maria; Svensson, Martin.
I: Monatshefte fur Mathematik, Bind 190, Nr. 4, 01.12.2019, s. 599-614.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review
TY - JOUR
T1 - Continuous deformations of harmonic maps and their unitons
AU - Aleman, Alexandru
AU - Martín, María J.
AU - Persson, Anna Maria
AU - Svensson, Martin
PY - 2019/1/28
Y1 - 2019/1/28
N2 - It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.
AB - It is known that any harmonic map of finite uniton number from a Riemann surface into U (n) can be deformed into a new harmonic map with an associated S1-invariant extended solution. We study this deformation in detail using operator-theoretic methods. In particular, we show that the corresponding unitons are real analytic functions of the deformation parameter, and that the deformation is closely related to the Bruhat decomposition of the corresponding extended solution.
KW - Blaschke–Potapov products
KW - Bruhat decomposition
KW - Extended solutions
KW - Harmonic maps
KW - Shift-invariant subspaces
KW - Unitons
U2 - 10.1007/s00605-019-01265-x
DO - 10.1007/s00605-019-01265-x
M3 - Journal article
VL - 190
SP - 599
EP - 614
JO - Monatshefte für Mathematik
JF - Monatshefte für Mathematik
SN - 0026-9255
IS - 4
ER -