The Thresholding Scheme for Mean Curvature Flow and De Giorgi's Ideas for Gradient Flows

Explore a seminar on the analysis and methods of partial differential equations, focusing on mean curvature flow and gradient flows. Delve into Felix Otto's presentation on "The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows." Examine the multi-phase version of interface flow by mean curvature in the context of grain growth in polycrystalline materials. Learn about the computationally efficient thresholding scheme for mean curvature flow by Osher et al. and its extension to multi-phase situations with surface tensions dependent on lattice mismatch. Understand the gradient flow structure of mean curvature flow and the interpretation of the thresholding scheme as a "minimizing movements" scheme. Investigate the conditional convergence proof based on De Giorgi's ideas for gradient flows in metric spaces, drawing parallels to the convergence proof for the minimizing movement scheme by Almgren, Taylor, and Wang.