Continuous deformations of harmonic maps and their unitons

Research output: Contribution to journalArticle

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.

Details

Authors
Organisations
External organisations
  • Autonomous University of Madrid
  • University of Southern Denmark
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Blaschke–Potapov products, Bruhat decomposition, Extended solutions, Harmonic maps, Shift-invariant subspaces, Unitons
Original languageEnglish
JournalMonatshefte fur Mathematik
Publication statusPublished - 2019 Jan 28
Publication categoryResearch
Peer-reviewedYes