Globality of the DPW construction for Smyth potentials in the case of SU(1,1)
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910721298661376 |
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| author | Udagawa, Tadashi |
| author_facet | Udagawa, Tadashi |
| 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_13331 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Globality of the DPW construction for Smyth potentials in the case of SU(1,1) Udagawa, Tadashi Differential Geometry 53A10, 35Q15 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). |
| title | Globality of the DPW construction for Smyth potentials in the case of SU(1,1) |
| topic | Differential Geometry 53A10, 35Q15 |
| url | https://arxiv.org/abs/2310.13331 |