JournalsifbVol. 11 , No. 1DOI 10.4171/ifb/207

Level set approach for fractional mean curvature flows

  • Cyril Imbert

    Université Paris-Est Créteil Val de Marne, France
Level set approach for fractional mean curvature flows cover

Abstract

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 phasefield 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.