We consider a variational scheme for the anisotropic (including crystalline) mean curvature flow of sets with strictly positive curvature. show that such condition is preserved by scheme, and we prove strict convergence in BV time-integrated perimeters approximating evolutions, extending recent result De Philippis Laux to setting. also uniqueness flat obtained limit.

A hyperbolic flow by mean curvature equation, l t #cv"i, for the evolution of interfaces is studied. Here v, i and l t are the normal velocity, curvature and normal acceleration of the interface. A crystalline algorithm is developed for the motion of closed convex polygonal curves; such curves may exhibit damped oscillations and their shape appears to rotate during the evolutionary process. The...

We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme. Assuming the regularity of the obstacles, in the two-dimensional case we show existence and uniqueness of a regular solution before the onset of singularities. Finally, we discuss a...

We obtain the evolution equations for the Riemann tensor, the Ricci tensor and the scalar curvature induced by the mean curvature flow. The evolution for the scalar curvature is similar to the Ricci flow, however, negative, rather than positive, curvature is preserved. Our results are valid in any dimension.

the study of flow in compound channels with vegetated floodplains is essential to assessing the development of the stage-discharge relationship and sediment and pollutant transport. the present study experimentally investigated mean flow and turbulence characteristics in a prismatic compound channel. the experimental program consisted of vegetated and non-vegetated floodplains with different re...