Saved in:
Bibliographic Details
Main Author: Udagawa, Tadashi
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2310.13331
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We construct harmonic maps into SU(1,1)/U(1) starting from Smyth potentials ξ, by the DPW method, In this method, harmonic maps are obtained from the Iwasawa factorization of a solution L of L^{-1} dL = ξ. However, the Iwasawa factorization in the case of a noncompact group is not always global. We show that L can be expressed in terms of Bessel functions and from the asymptotic expansion of Bessel functions we solve a Riemann-Hilbert problem to give a global Iwasawa factorization. In this way we give a more direct proof of the globality of our solution than in the work of Dorfmeister-Guest-Rossman (2010), while avoiding the general isomonodromy theory used by Guest-Its-Lin (2015).