تقرير
On the size of the singular set of minimizing harmonic maps into the 2-sphere in dimension four and higher
| العنوان: | On the size of the singular set of minimizing harmonic maps into the 2-sphere in dimension four and higher |
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| المؤلفون: | Mazowiecka, Katarzyna, Miśkiewicz, Michał, Schikorra, Armin |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematics - Differential Geometry |
| الوصف: | We extend the results of our recent preprint [arXiv: 1811.00515] into higher dimensions $n \geq 4$. For minimizing harmonic maps $u\in W^{1,2}(\Omega,\mathbb{S}^2)$ from $n$-dimensional domains into the two dimensional sphere we prove: (1) An extension of Almgren and Lieb's linear law, namely \[\mathcal{H}^{n-3}(\textrm{sing} u) \le C \int_{\partial \Omega} |\nabla_T u|^{n-1} \,d\mathcal{H}^{n-1};\] (2) An extension of Hardt and Lin's stability theorem, namely that the size of singular set is stable under small perturbations in $W^{1,n-1}$ norm of the boundary. Comment: 33 pages, 1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1902.03161 |
| رقم الأكسشن: | edsarx.1902.03161 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |