Continuous deformations of harmonic maps and their unitons

Alexandru Aleman, María J. Martín*, Anna Maria Persson, Martin Svensson

*Kontaktforfatter for dette arbejde

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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.

OriginalsprogEngelsk
TidsskriftMonatshefte fur Mathematik
Vol/bind190
Udgave nummer4
Sider (fra-til)599-614
Antal sider16
ISSN0026-9255
DOI
StatusE-pub ahead of print - 28. jan. 2019

Fingeraftryk

Harmonic Maps
Bruhat Decomposition
Real Analytic Functions
Riemann Surface
Invariant
Operator

Citer dette

Aleman, Alexandru ; Martín, María J. ; Persson, Anna Maria ; Svensson, Martin. / Continuous deformations of harmonic maps and their unitons. I: Monatshefte fur Mathematik. 2019 ; Bind 190, Nr. 4. s. 599-614.
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keywords = "Blaschke–Potapov products, Bruhat decomposition, Extended solutions, Harmonic maps, Shift-invariant subspaces, Unitons",
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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 tidsskriftTidsskriftartikelForskningpeer 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 -