论文标题
大地直径的先验界限。第二部分。 Varifolds的精细连接性能
A priori bounds for geodesic diameter. Part II. Fine connectedness properties of varifolds
论文作者
论文摘要
对于第一个变化通过集成表示的Varifolds，我们介绍了与局部Lipschitzian真实有价值函数的不可分解性的概念。与不可塑性不同，这种较弱的连接性属性是由与本集，$ g $链和沉浸的几何变量问题相关的varifolds继承的；然而，它足够强大，可以随后从其中扣除实质性的几何后果。我们目前的研究基于本文提出的几个概念：其中的一般有限变化的实际有价值函数，一般的分区，沿实际有价值的广义弱化功能的分区，尤其是局部分解的局部有限性。
For varifolds whose first variation is representable by integration, we introduce the notion of indecomposability with respect to locally Lipschitzian real valued functions. Unlike indecomposability, this weaker connectedness property is inherited by varifolds associated with solutions to geometric variational problems phrased in terms of sets, $G$ chains, and immersions; yet it is strong enough for the subsequent deduction of substantial geometric consequences therefrom. Our present study is based on several further concepts for varifolds put forward in this paper: real valued functions of generalised bounded variation thereon, partitions thereof in general, partition thereof along a real valued generalised weakly differentiable function in particular, and local finiteness of decompositions.
