论文标题
公制图中的Cheeger Cut和Cheeger问题
The Cheeger Cut and Cheeger Problem in Metric Graphs
论文作者
论文摘要
对于离散的加权图，有足够的文献有关Cheeger Cut和Cheeger问题，但是对于度量图，这些问题的结果很少。我们的目的是研究公制图中的Cheeger剪切和Cheeger问题。为此，我们在\ cite {mazon}中引入的度量图中使用总变化和周长的概念，该图表考虑了有界变化函数的顶点的跳跃。此外，我们研究了度量图中的减去$ 1 $ laplacian运算符的特征值问题，从而提供了一种解决最佳cheeger剪切问题的方法。
For discrete weighted graphs there is sufficient literature about the Cheeger cut and the Cheeger problem, but for metric graphs there are few results about these problems. Our aim is to study the Cheeger cut and the Cheeger problem in metric graphs. For that, we use the concept of total variation and perimeter in metric graphs introduced in \cite{Mazon}, which takes into account the jumps at the vertices of the functions of bounded variation. Moreover, we study the eigenvalue problem for the minus $1$-Laplacian operator in metric graphs, whereby we give a method to solve the optimal Cheeger cut problem.
