Our goal in this paper is to find an estimate for the spectral gap of the Laplacian on a 2-simplicial complex consisting on a triangulation of a complete graph. An upper estimate is given by generalizing the Cheeger constant. The lower estimate is obtained from the first non-zero eigenvalue of the discrete Laplacian acting on the functions of certain sub-graphs.

中文翻译：

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三角剖分上离散拉普拉斯算子的光谱间隙

我们在本文中的目标是在由完整图的三角剖分构成的 2-单纯复形上找到拉普拉斯算子谱间隙的估计。通过推广 Cheeger 常数给出了一个上估计值。较低的估计是从离散拉普拉斯算子的第一个非零特征值中获得的，该特征值作用于某些子图的函数。