Mathematics

In this talk, we analyze the asymptotic of a time-discrete approximation of the volume preserving fractional mean curvature flow.
More precisely, we prove that the discrete flow starting from any bounded set of finite fractional perimeter converges exponentially fast to a single ball when the dimension N ≤ 7 and the fractional exponent s ≈ 1, or for any s ∈ (0,1) when N=2.
As an intermediate result we show a fractional quantitative Alexandrov-type estimate for normal deformations of a ball.