Download E-books Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations (Publications of the Scuola Normale Superiore) PDF
By Giovanni Bellettini
The purpose of the publication is to review a few points of geometric evolutions, corresponding to suggest curvature movement and anisotropic suggest curvature move of hypersurfaces. We study the foundation of such flows and their geometric and variational nature. the most vital points of suggest curvature movement are defined, comparable to the comparability precept and its use within the definition of compatible susceptible suggestions. The anisotropic evolutions, which are regarded as a generalization of suggest curvature stream, are studied from the view element of Finsler geometry. referring to singular perturbations, we talk about the convergence of the Allen–Cahn (or Ginsburg–Landau) style equations to (possibly anisotropic) suggest curvature stream prior to the onset of singularities within the restrict challenge. We research such sorts of asymptotic difficulties additionally within the static case, exhibiting convergence to prescribed curvature-type difficulties.