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Anisotropic motion by mean curvature in the context of Finsler geometry. (English) Zbl 0873.53011
Author’s abstract: “We study the anisotropic motion of a hypersurface in the context of the geometry of Finsler spaces. This amounts to 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 \(\phi\) 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 approaches, such as the variational method of Almgren-Taylor-Wang, the Hamilton-Jacobi equation, and the approximation by means of a reaction-diffusion equation”.
Reviewer: N.L.Youssef (Giza)

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
49Q20 Variational problems in a geometric measure-theoretic setting
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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