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Continuous deformations of harmonic maps and their unitons

Aleman, Alexandru LU ; Martín, María J. ; Persson, Anna Maria LU and Svensson, Martin LU (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.

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author
; ; and
organization
publishing date
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}},
}