Geometry

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 check a few points of geometric evolutions, resembling suggest curvature move and anisotropic suggest curvature stream of hypersurfaces. We study the foundation of such flows and their geometric and variational nature. one of the most vital points of suggest curvature stream are defined, akin to the comparability precept and its use within the definition of appropriate susceptible strategies. The anisotropic evolutions, that are regarded as a generalization of suggest curvature circulation, are studied from the view aspect of Finsler geometry. bearing on singular perturbations, we talk about the convergence of the Allen–Cahn (or Ginsburg–Landau) style equations to (possibly anisotropic) suggest curvature circulation sooner than the onset of singularities within the restrict challenge. We research such different types of asymptotic difficulties additionally within the static case, exhibiting convergence to prescribed curvature-type difficulties.

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