تقرير
Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation
| العنوان: | Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation |
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| المؤلفون: | Ding, Qi, Jost, J., Xin, Y. L. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry |
| الوصف: | For any $\Lambda>0$, let $\mathcal{M}_{n,\Lambda}$ denote the space containing all locally Lipschitz minimal graphs of dimension $n$ and of arbitrary codimension $m$ in Euclidean space $\mathbb{R}^{n+m}$ with uniformly bounded 2-dilation $\Lambda$ of their graphic functions. In this paper, we show that this is a natural class to extend structural results known for codimension one. In particular, we prove that any tangent cone $C$ of $M\in\mathcal{M}_{n,\Lambda}$ at infinity has multiplicity one. This enables us to get a Neumann-Poincar$\mathrm{\acute{e}}$ inequality on stationary indecomposable components of $C$. A corollary is a Liouville theorem for $M$. For small $\Lambda>1$(we can take any $\Lambda<\sqrt{2}$), we prove that (i) for $n\leq7$, $M$ is flat; (2) for $n>8$ and a non-flat $M$, any tangent cone of $M$ at infinity is a multiplicity one quasi-cylindrical minimal cone in $\mathbb{R}^{n+m}$ whose singular set has dimension $\leq n-7$. Comment: 56 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.09383 |
| رقم الأكسشن: | edsarx.2109.09383 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |