  This paper is concerned with the study of a geometric flow whose law involves
a singular integral operator. This operator is used to define a non-local mean
curvature of a set. Moreover the associated flow appears in two important
applications: dislocation dynamics and phase field theory for fractional
reaction-diffusion equations. It is defined by using the level set method. The
main results of this paper are: on one hand, the proper level set formulation
of the geometric flow; on the other hand, stability and comparison results for
the geometric equation associated with the flow.
