Paper detail

De Giorgi's inequality for the thresholding scheme with arbitrary mobilities and surface tensions

We provide a new convergence proof of the celebrated Merriman-Bence-Osher scheme for multiphase mean curvature flow. Our proof applies to the new variant incorporating a general class of surface tensions and mobilities, including typical choices for modeling grain growth. The basis of the proof are the minimizing movements interpretation of Esedoğlu and Otto and De Giorgi's general theory of gradient flows. Under a typical energy convergence assumption we show that the limit satisfies a sharp energy-dissipation relation.