论文标题
通过抽象分解原理对正常可区分G链的设定分类
Set-decomposition of normal rectifiable G-chains via an abstract decomposition principle
论文作者
论文摘要
我们介绍了正常G-Flat链的设定分解概念。我们表明，任何正常的纠正$ G $ -FLAT链都可以在设置不可兼容的子链中进行分解。这概括了由于Ambrosio，Caselles，Masnou和Morel引起的``测量理论''相互关联的组件的分解。它也可以看作是费德勒（Federer）在不可分解的组件中积分电流分解的变体。与先前的结果相反，我们不认为g有限地紧凑。因此，我们不能依靠具有均匀界限的N-字符的链序列的紧凑性。我们从新的抽象分解原理中得出结果。与较早的证据一样，中央成分是等等不平等的有效性。我们在此处使用一些H-MAS的有限性来替代完整性。
We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite perimeter in their ``measure theoretic'' connected components due to Ambrosio, Caselles, Masnou and Morel. It can also be seen as a variant of the decomposition of integral currents in indecomposable components by Federer.As opposed to previous results, we do not assume that G is boundedly compact. Therefore we cannot rely on the compactness of sequences of chains with uniformly bounded N-norms. We deduce instead the result from a new abstract decomposition principle. As in earlier proofs a central ingredient is the validity of an isoperimetric inequality. We obtain it here using the finiteness of some h-mass to replace integrality.
