Anisotropic motion by mean curvature in the context of Finsler geometry

Maurizio Paolini, Giovanni Bellettini, G. Bellettini

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

125 Citazioni (Scopus)

Abstract

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

Keywords

  • Finsler geometry
  • anisotropy

Fingerprint

Entra nei temi di ricerca di 'Anisotropic motion by mean curvature in the context of Finsler geometry'. Insieme formano una fingerprint unica.

Cita questo