Title
Jump sets of BV mappings between metric spaces
Abstract
After discussing a suitable definition of the variation energy for mappings between a metric measure space and a metric space we will introduce a notion of jump point equivalent to that of a point of non-approximate continuity. Thanks to the metric nature of this definition and the theory of sets of finite perimeter we will prove, for a map of bounded variation, the uniform finiteness of jump values (i.e., values attained at a positive density) for codimension 1 a.e. jump point whenever the source space is doubling and supports a 1-PI and the target space is complete and compact.
