论文标题
Kirchhoff Laplacian的上部特征值界限
Upper Eigenvalue Bounds for the Kirchhoff Laplacian on Embbeded Metric Graphs
论文作者
论文摘要
我们根据图的属G属的属于紧凑的度量图，在紧凑的度量图上得出了基尔chhofflaplacian的特征值的上限。如果$ g = 0 $，即公制图是平面，则可以进一步改善这些界限。我们的结果基于Kirchhoff Laplacian和特定某种组合加权Laplacian之间的光谱对应关系。为了利用这种对应关系，我们还证明了对加权组合laplacians的特征值的新估计，这些估计值以前仅在加权情况下才知道。
We derive upper bounds for the eigenvalues of the Kirchhoff Laplacian on a compact metric graph depending on the graph's genus g. These bounds can be further improved if $g = 0$, i.e. if the metric graph is planar. Our results are based on a spectral correspondence between the Kirchhoff Laplacian and a particular a certain combinatorial weighted Laplacian. In order to take advantage of this correspondence, we also prove new estimates for the eigenvalues of the weighted combinatorial Laplacians that were previously known only in the weighted case.
