Continuous deformations of harmonic maps and their unitons

  • Alexandru Aleman
  • María J. MartínEmail author
  • Anna-Maria Persson
  • Martin Svensson


It is known that any harmonic map of finite uniton number from a Riemann surface into \(\mathrm {U}(n)\) can be deformed into a new harmonic map with an associated \(S^1\)-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.


Harmonic maps Bruhat decomposition Extended solutions Unitons Shift-invariant subspaces Blaschke–Potapov products 

Mathematics Subject Classification

58E20 47A56 



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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Alexandru Aleman
    • 1
  • María J. Martín
    • 2
    Email author
  • Anna-Maria Persson
    • 1
  • Martin Svensson
    • 3
  1. 1.Department of MathematicsUniversity of LundLundSweden
  2. 2.Departamento de Matemáticas, Facultad de Ciencias (Módulo 17)Universidad Autónoma de MadridMadridSpain
  3. 3.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark

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