Report
Harmonic maps of punctured surfaces to the hyperbolic plane
| العنوان: | Harmonic maps of punctured surfaces to the hyperbolic plane |
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| المؤلفون: | Huang, Andy C. |
| سنة النشر: | 2016 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Geometric Topology |
| الوصف: | In this paper, we construct polynomial growth harmonic maps from once-punctured Riemann surfaces of any finite genus to any even-sided, regular, ideal polygon in the hyperbolic plane. We also establish their uniqueness within a class of maps which differ by exponentially decaying variations. Previously, harmonic maps from once-punctured spheres to the hyperbolic plane have been parameterized by holomorphic quadratic differentials on the complex plane. Our harmonic maps, mapping a genus g>1 domain to a k-sided polygon, correspond to meromorphic quadratic differentials having one pole of order (k+2) and (4g+k-2) zeros (counting multiplicity). In this way, we can associate to these maps a holomorphic quadratic differential on the punctured Riemann surface domain. As an example, we specialize our theorems to obtain a harmonic map from a punctured square torus to an ideal square, and deduce the five possibilities for the divisor of its Hopf differential. Comment: 45 pages, 9 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1605.07715 |
| رقم الانضمام: | edsarx.1605.07715 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |