论文标题
离散体积保留平均曲率流的长时间行为
Long Time Behaviour of the Discrete Volume Preserving Mean Curvature Flow in the Flat Torus
论文作者
论文摘要
我们表明，在平坦的圆环$ \ mathbb {t}^n $中，离散的近似体积保留平均曲率流在靠近严格稳定的临界集合$ e $的情况下，长期以来会收敛到$ e $ $ e $的翻译。作为中间结果，我们为周期性稳定的恒定平均曲率超出表面建立了Alexandrov类型的新定量估计。最后，在两个维度的情况下，提供了具有任意初始的有限周长集的离散流的长时间行为的完整表征。
We show that the discrete approximate volume preserving mean curvature flow in the flat torus $\mathbb{T}^N$ starting near a strictly stable critical set $E$ of the perimeter converges in the long time to a translate of $E$ exponentially fast. As an intermediate result we establish a new quantitative estimate of Alexandrov type for periodic strictly stable constant mean curvature hypersurfaces. Finally, in the two dimensional case a complete characterization of the long time behaviour of the discrete flow with arbitrary initial sets of finite perimeter is provided.
