Continuous deformations of harmonic maps and their unitons
(2019) In Monatshefte fur Mathematik- 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/842182f8-baaf-48a8-a93f-b4c49c44a694
- author
- Aleman, Alexandru LU ; Martín, María J. ; Persson, Anna Maria LU and Svensson, Martin LU
- organization
- publishing date
- 2019-01-28
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Blaschke–Potapov products, Bruhat decomposition, Extended solutions, Harmonic maps, Shift-invariant subspaces, Unitons
- in
- Monatshefte fur Mathematik
- publisher
- Springer
- external identifiers
-
- scopus:85060753678
- ISSN
- 0026-9255
- DOI
- 10.1007/s00605-019-01265-x
- language
- English
- LU publication?
- yes
- id
- 842182f8-baaf-48a8-a93f-b4c49c44a694
- date added to LUP
- 2019-02-13 08:34:14
- date last changed
- 2022-04-25 21:37:01
@article{842182f8-baaf-48a8-a93f-b4c49c44a694, abstract = {{<p>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 S<sup>1</sup>-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.</p>}}, author = {{Aleman, Alexandru and Martín, María J. and Persson, Anna Maria and Svensson, Martin}}, issn = {{0026-9255}}, keywords = {{Blaschke–Potapov products; Bruhat decomposition; Extended solutions; Harmonic maps; Shift-invariant subspaces; Unitons}}, language = {{eng}}, month = {{01}}, publisher = {{Springer}}, series = {{Monatshefte fur Mathematik}}, title = {{Continuous deformations of harmonic maps and their unitons}}, url = {{http://dx.doi.org/10.1007/s00605-019-01265-x}}, doi = {{10.1007/s00605-019-01265-x}}, year = {{2019}}, }