论文标题
$ k $ Mean-convex和$ k $ - 以最小化套件
$K$ mean-convex and $K$-outward minimizing sets
论文作者
论文摘要
我们考虑通过非局部平均曲率的集合的演变，并讨论了两个几何特性的流动，这是平均凸度和外部最小值。 我们分析中的主要工具是级别设置公式和非本地流动的最小化运动方案。当初始集对外最小化时，我们还显示了离散演变的（时间积分）非局部周围的（时间积分）与极限流的非局部周长的收敛。
We consider the evolution of sets by nonlocal mean curvature and we discuss the preservation along the flow of two geometric properties, which are the mean convexity and the outward minimality. The main tools in our analysis are the level set formulation and the minimizing movement scheme for the nonlocal flow. When the initial set is outward minimizing, we also show the convergence of the (time integrated) nonlocal perimeters of the discrete evolutions to the nonlocal perimeter of the limit flow.
