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We consider in ${ℝ}^2$ all curvature equation $\frac{\partial u}{\partial t}=\left|Du\right|G\left(\mathrm{curv}\left(u\right)\right)$ where is a nondecreasing function and curv() is the curvature of the level line passing by . These equations are invariant with respect to any contrast change , with nondecreasing. Consider the contrast invariant operator $T_t:u_o\to u\left(t\right)$. A Matheron theorem asserts that all contrast invariant operator can be put in a form $\left(Tu\right)\left(𝐱\right)={inf}_{B\in ℬ}{sup}_{𝐲\in B}u(𝐱+𝐲)$. We show the asymptotic equivalence of both formulations. More precisely, we show that all curvature equations can be obtained as the iteration...

We investigate the approximation of the evolution of compact hypersurfaces of ${ℝ}^N$ depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.

We investigate the approximation of the evolution of compact hypersurfaces of ${ℝ}^N$ depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by the surface.