A notion of s-fractional mass for 1-currents

This talk is about a generalization of the s-fractional perimeter: we give a short introduction to the subject, explain the approach of a possible generalization of the s-fractional perimeter to objects with arbitrary codimension, and define it in the setting of 1-currents in N-space.
In addition, we give some of the basic properties of this notion of s-fractional-mass.
Based on a joint work with Marco Cicalese, Andrea Kubin, Fumihiko Onoue and Marcello Ponsiglione.