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 \({\mathbf {R}}^n \setminus \Gamma \), where \(\Gamma \) 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.

我们证明了一个拟最小化序列的弱极限是一个拟最小集合。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。这个结果也类似于局部Hausdorff收敛中David的极限定理。该证明基于适当变形的构造，并且不限于周围空间\（{\ mathbf {R}} ^ n \ setminus \ Gamma \），其中\（\ Gamma \）是边界。我们推导了一种直接方法来解决各种高原问题，甚至最大程度地减少了竞争对手与边界的交集。此外，我们提出了一种构建费德勒-弗莱明投影的结构，以及对投影中心选择的新估计。