Abstract
Signed distance from a smooth boundary.- Mean curvature vector and second fundamental form.- First variations of volume integrals and of the perimeter.- Smooth mean curvature flows.- Huisken's monotonicity formula.- Inclusion principle. Local well posedness: the approach of Evans-Spruck.- Grayson's example.- De Giorgi's barriers.- Inner and outer regularizations.- An example of fattening.- Ilmanen's interposition lemma.- The avoidance principle.- Comparison between barriers and a generalized evolution.- Barriers and level set evolution.- Parabolic singular perturbations: formal matched asymptotics, convergence and error estimate.
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