论文标题
连接laplacian镜头的近似
Approximations of the connection Laplacian spectra
论文作者
论文摘要
我们考虑了矢量束上的卷积型运算符，上面是度量量的空间。该操作员将类似的卷积拉普拉斯（Laplacian）扩展到我们早期工作中的功能上，并将其扩展到矢量束，并且是图形连接laplacian的自然扩展。我们证明，对于封闭的riemannian歧管上的欧几里得或遗传学连接，该操作员的频谱和图形连接laplacian的频谱都近似于连接laplacian的光谱。
We consider a convolution-type operator on vector bundles over metric-measure spaces. This operator extends the analogous convolution Laplacian on functions in our earlier work to vector bundles, and is a natural extension of the graph connection Laplacian. We prove that for Euclidean or Hermitian connections on closed Riemannian manifolds, the spectrum of this operator and that of the graph connection Laplacian both approximate the spectrum of the connection Laplacian.
