Continuous deformations of harmonic maps and their unitons

Alexandru Aleman; María J. Martín; Anna Maria Persson; Martin Svensson

doi:10.1007/s00605-019-01265-x

Continuous deformations of harmonic maps and their unitons

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

^*Kontaktforfatter for dette arbejde

Institut for Matematik og Datalogi

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

Abstrakt

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	https://doi.org/10.1007/s00605-019-01265-x
Status	Udgivet - 1. dec. 2019

Dokumenter og links

10.1007/s00605-019-01265-x

https://arxiv.org/pdf/1702.06171.pdf

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Citationsformater

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abstract = "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.",

keywords = "Blaschke–Potapov products, Bruhat decomposition, Extended solutions, Harmonic maps, Shift-invariant subspaces, Unitons",

author = "Alexandru Aleman and Mart{\'i}n, {Mar{\'i}a J.} and Persson, {Anna Maria} and Martin Svensson",

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T1 - Continuous deformations of harmonic maps and their unitons

AU - Aleman, Alexandru

AU - Martín, María J.

AU - Persson, Anna Maria

AU - Svensson, Martin

PY - 2019/12/1

Y1 - 2019/12/1

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

AN - SCOPUS:85060753678

VL - 190

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EP - 614

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

SN - 0026-9255

IS - 4

ER -