This paper introduces a notion of decompositions of integral varifolds into countably many integral varifolds, and the existence of such decomposition of integral varifolds whose first variation is representable by integration is established. However, the decompositions may fail to be unique. Furthermore, this result can be generalized by replacing the class of integral varifolds with some classes of rectifiable varifolds whose density is uniformly bounded from below; for these classes, we also prove a general version of the compactness theorem for integral varifolds.

中文翻译：

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多样性的积分分解

本文引入了积分varifold分解为可数个积分varifold的概念，并证明了其一阶变分可以用积分表示的积分varifold分解的存在性。然而，分解可能不是唯一的。此外，这个结果可以通过用一些密度从下面均匀有界的可整流varifolds类替换积分varifolds类来推广；对于这些类，我们还证明了积分varifolds 紧性定理的一般版本。