I prove that the spectrum of the Laplace–Beltrami operator with the Neumann boundary condition on a compact Riemannian manifold with boundary admits a fast approximation by the spectra of suitable graph Laplacians on proximity graphs on the manifold, and similar graph approximation works for metric-measure spaces glued out of compact Riemannian manifolds of the same dimension.

中文翻译：

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拉普拉斯光谱的图形近似

我证明了具有边界的紧黎曼流形上具有 Neumann 边界条件的 Laplace-Beltrami 算子的谱允许通过流形上的邻近图上合适的图拉普拉斯算子的谱进行快速近似，并且类似的图逼近适用于度量测量空间由相同维度的紧凑黎曼流形粘合而成。