# zbMATH — the first resource for mathematics

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)

##### MSC:
 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
##### Keywords:
anisotropic motion of a hypersurface; Finsler spaces
Full Text: