We address in this paper the study of a geometric evolution, corresponding to a curvature which is non-local and singular at the origin. The curvature represents the first variation of the energy Mρ(E) defined in (1.1), proposed in a recent work [5] as a variant of the standard perimeter penalization for the denoising of nonsmooth curves. To deal with such degeneracies, we first give an abstrac...