A general criterion for jump set slicing and applications

In this paper a novel criterion for the slicing of the jump set of a function is provided, which bypasses the codimension-one and the parallelogram law techniques developed in $BD$-spaces. The approach builds upon a recent rectifiability result of integralgeometric measures and is further applied to the study of the structure of the jump set of functions with generalized bounded deformation in a Riemannian setting.