论文标题
准序列序列的弱极限
Weak limits of quasiminimizing sequences
论文作者
论文摘要
我们表明，准序列序列的弱极限是准集合。这概括了De Lellis，de Philippis，de Rosa，Ghiraldin和Maggi引入的最小化序列的弱极限的概念。该结果也类似于局部Hausdorff收敛中David的限制定理。证明是基于合适变形的构造，不限于环境空间$ \ mathbb {r}^n \setMinusγ$，其中$γ$是边界。我们推断出一种直接解决各种平稳问题的方法，甚至最大程度地减少了竞争对手与边界的交集。此外，我们提出了一种建立Federer的结构，包括对投影中心选择的新估计。
We show that the weak limit of a quasiminimizing sequence is a quasiminimal set. This generalizes the notion of weak limit of a minimizing sequences introduced by De Lellis, De Philippis, De Rosa, Ghiraldin and Maggi. This result is also analogous to the limiting theorem of David in local Hausdorff convergence. The proof is based on the construction of suitable deformations and is not limited to the ambient space $\mathbb{R}^n \setminus Γ$, where $Γ$ is the boundary. We deduce a direct method to solve various Plateau problems, even minimizing the intersection of competitors with the boundary. Furthermore, we propose a structure to build Federer--Fleming projections as well as a new estimate on the choice of the projection centers.
