A general criterion for jump set slicing and applications

TL;DR

This paper introduces a new criterion for slicing the jump set of functions, avoiding traditional techniques, and applies it to analyze the structure of functions with generalized bounded deformation on Riemannian manifolds.

Contribution

It presents a novel criterion for jump set slicing that bypasses classical methods and extends analysis to Riemannian settings.

Findings

New criterion for jump set slicing developed

Application to functions with generalized bounded deformation

Extension of results to Riemannian manifolds

Abstract

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.