Anisotropic motion by mean curvature in the context of Finsler geometry

G. Bellettini, Maurizio Paolini, Giovanni Bellettini

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125 Citazioni (Scopus)


We study the anisotropic motion of a hypersurface in the context of the geometry of Finsler spaces. This amounts in considering the evolution in relative geometry, where all quantities are referred to the given Finsler metric $\phi$ representing the anisotropy, which we allow to be a function of space. Assuming that the anisotropy is strictly convex and smooth, we prove that the natural evolution law is of the form "velocity = $H_\phi$", where $H_\phi$ is the relative mean curvature vector of the hypersurface. We derive this evolution law using different approches, such as the variational method of Almgren-Taylor-Wang, the Hamilton-Jacobi equation, and the approximation by means of a reaction-diffusion equation.
Lingua originaleEnglish
pagine (da-a)537-566
Numero di pagine30
RivistaHokkaido Mathematical Journal
Stato di pubblicazionePubblicato - 1996


  • Finsler geometry
  • anisotropy


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