论文标题
非本地几何发展的稳定性结果，并限制了分数平均曲率流的情况
Stability results for nonlocal geometric evolutions and limit cases for fractional mean curvature flows
论文作者
论文摘要
我们为局部和非局部曲率引入了统一收敛的概念。然后，我们提出了一种抽象方法，以证明在级别设置公式中的相应几何流量的收敛性。我们应用这样的一般理论来表征$ s $属性平均曲率流动为$ s \ to 0^+$和$ s \ to 1^ - $。与$ s $分类平均曲率流相比，我们介绍了$ s-riesz曲率流的概念，并将其极限描述为$ s \至0^ - $。最终，我们将限制行为讨论为$ r \至0^+$的$ r $ -Minkowski内容生成的流量。
We introduce a notion of uniform convergence for local and nonlocal curvatures. Then, we propose an abstract method to prove the convergence of the corresponding geometric flows, within the level set formulation. We apply such a general theory to characterize the limits of $s$-fractional mean curvature flows as $s\to 0^+$ and $s\to 1^-$. In analogy with the $s$-fractional mean curvature flows, we introduce the notion of $s$-Riesz curvature flows and characterize its limit as $s\to 0^-$. Eventually, we discuss the limit behavior as $r\to 0^+$ of the flow generated by a regularization of the $r$-Minkowski content.
