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.Comment: This is the second paper of a series of three papers which shall
supersede arXiv:1709.05504 by the same authors. 58 pages (v1: 43 pages), no
figures, added treatment of varifolds with free boundary which includes an
isoperimetric lower density ratio bound in 9.22 and results in Theorem E and
Corollary