تقرير
Globality of the DPW construction for Smyth potentials in the case of SU(1,1)
| العنوان: | Globality of the DPW construction for Smyth potentials in the case of SU(1,1) |
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| المؤلفون: | Udagawa, Tadashi |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53A10, 35Q15 |
| الوصف: | We construct harmonic maps into SU(1,1)/U(1) satrting from Smyth potentials \xi, by the DPW method, In this method, harmonic maps are obtained from the Iwasawa factorization of a solution L of L^{-1} dL = \xi. 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 than in the work of Dorfmeister-Guest-Rossman (2010), while avoiding the general isomonodromy theory used by Guest-Its-Lin (2015). Comment: 24 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.13331 |
| رقم الأكسشن: | edsarx.2310.13331 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |