تقرير
Finite type minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$
| العنوان: | Finite type minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ |
|---|---|
| المؤلفون: | Hauswirth, L., Kilian, M., Schmidt, M. U. |
| المصدر: | Illinois J. Math, 57 (3), 697-741, 2013 |
| سنة النشر: | 2012 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, 53A10 |
| الوصف: | We study minimal annuli in $\mathbb{S}^2 \times \mathbb{R}$ of finite type by relating them to harmonic maps $\mathbb{C} \to \mathbb{S}^2$ of finite type. We rephrase an iteration by Pinkall-Sterling in terms of polynomial Killing fields. We discuss spectral curves, spectral data and the geometry of the isospectral set. We consider polynomial Killing fields with zeroes and the corresponding singular spectral curves, bubbletons and simple factors. We investigate the differentiable structure on the isospectral set of any finite type minimal annulus. We apply the theory to a 2-parameter family of embedded minimal annuli foliated by horizontal circles. Comment: 30 pages. v2: Normalizations and minor typos fixed. Accepted for publication in Illinois J. Math |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1210.5606 |
| رقم الأكسشن: | edsarx.1210.5606 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |