论文标题
$ c^2 $ submanifold上的准临时套件和高原与Čech同源条件的问题
Quasiminimal sets and Plateau's problem with Čech homological conditions on $C^2$ submanifold
论文作者
论文摘要
令$ω\ subseteq \ mathbb {r}^n $为$ m $ dimensional封闭的$ c^2 $，$ d $的封闭submanifold是1至$ m $之间的正整数。我们将研究$ω$的准集合的几何和拓扑礼节，并表明最小化$ d $ sets的序列会收敛于弱拓扑的最小设置。随之而来的是，我们可以在$ω$上解决高原的尺寸$ d $的问题。
Let $Ω\subseteq \mathbb{R}^n$ be an $m$-dimensional closed submanifold of class $C^2$, $d$ be a positive integer between 1 and $m$. We will study the geometric and topological proprieties of quasiminimal sets in $Ω$, and show that a minimizing sequence of $d$-sets converges to a minimal set in the sense of weak topology. Following from that, we can solve the Plateau's problem of dimension $d$ on $Ω$ with Čech homological conditions.
