论文标题
平坦表面上的有限差方法，带有平坦的统一矢量束
Finite difference method on flat surfaces with a flat unitary vector bundle
论文作者
论文摘要
我们在与扁平统一载体束的半翻译表面与离散表面的离散化相关的离散表面与von noumann边界条件的laplacian延伸的频谱之间建立了渐近关系。 作为我们研究的一个有趣的副产品，我们在图表上定义的“几乎谐波”离散函数获得了HARNACK型估计，该功能近似于给定的表面。 本文的结果将稍后用于将跨越树木数量，跨越森林和加权循环跨越森林的渐近膨胀与相应的Zeta调节确定因素联系起来。
We establish an asymptotic relation between the spectrum of the discrete Laplacian associated to discretizations of a half-translation surface with a flat unitary vector bundle and the spectrum of the Friedrichs extension of the Laplacian with von Neumann boundary conditions. As an interesting byproduct of our study, we obtain Harnack-type estimates on "almost harmonic" discrete functions, defined on the graphs, which approximate a given surface. The results of this paper will be later used to relate the asymptotic expansion of the number of spanning trees, spanning forests and weighted cycle-rooted spanning forests on the discretizations to the corresponding zeta-regularized determinants.
