تقرير
Higher codimension relative isoperimetric inequality outside a convex set
| العنوان: | Higher codimension relative isoperimetric inequality outside a convex set |
|---|---|
| المؤلفون: | Krummel, Brian |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, 49Q20 |
| الوصف: | We consider an isoperimetric inequality for $(m+1)$-dimensional area minimizing submanifolds of arbitrary codimension which lie outside a convex set $\mathcal{K} \subset \mathbb{R}^{n+1}$ and are bounded by a submanifold of $\mathbb{R}^{n+1} \setminus \mathcal{K}$ and the convex set $\mathcal{K}$. We show that the least value of the isoperimetric ratio is attained for an $(m+1)$-dimensional flat half-disk of $\mathbb{R}^{n+1}_+$. This extends prior work of Choe, Ghomi, and Ritor\'{e} in codimension one and proves a conjecture of Choe in the case of relative area minimizers. Comment: 55 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1710.04821 |
| رقم الأكسشن: | edsarx.1710.04821 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |