论文标题
通过非局部定量定理的离散体积的分数平均曲率流的渐近分数平均曲率流
Asymptotic of the Discrete Volume-Preserving Fractional Mean Curvature Flow via a Nonlocal Quantitative Alexandrov Theorem
论文作者
论文摘要
我们表征了保留分数平均曲率流的体积的离散时间近似的长时间行为。特别是，我们证明了从任何有限的一组有限分数范围开始的离散流程将成倍地收敛到单个球。作为中间结果，我们在分数设置中建立了定量的Alexandrov类型估计值，以实现球的正常变形。最后，当时间离散参数趋于零时，我们将扁平流的存在作为离散流的限制点。
We characterize the long time behaviour of a discrete-in-time approximation of the volume preserving fractional mean curvature flow. In particular, we prove that the discrete flow starting from any bounded set of finite fractional perimeter converges exponentially fast to a single ball. As an intermediate result we establish a quantitative Alexandrov type estimate in the fractional setting for normal deformations of a ball. Finally, we provide existence for flat flows as limit points of the discrete flow when the time discretization parameter tends to zero.
