论文标题
存在较弱的解决方案，以保留较高维度的平均曲率流量
Existence of weak solution to volume preserving mean curvature flow in higher dimensions
论文作者
论文摘要
在本文中，我们构建了一个整体varifolds的家族，这是$ l^2 $流的含义的全球薄弱解决方案。当初始数据的周长足够接近具有相同体积的球时，该流量也是短时间分布的BV-solution。为了构建流量，我们使用了由Mugnai，Seis和Spadaro的研究动机的非本地术语的Allen-cahn方程，以及Kim和Kwon。我们证明了allen-cahn方程的解决方案与整体varifolds家族的收敛性，只有自然假设对初始数据。
In this paper, we construct a family of integral varifolds, which is a global weak solution to the volume preserving mean curvature flow in the sense of $L^2$-flow. This flow is also a distributional BV-solution for a short time, when the perimeter of the initial data is sufficiently close to that of ball with the same volume. To construct the flow, we use the Allen--Cahn equation with non-local term motivated by studies of Mugnai, Seis, and Spadaro, and Kim and Kwon. We prove the convergence of the solution for the Allen--Cahn equation to the family of integral varifolds with only natural assumptions for the initial data.
