Approximations of the connection Laplacian spectra

2020/12/18 by Dmitri Burago, Burago, Dmitri, Sergei Ivanov +5 · 1 citation
Computer Science · Mathematics · Medicine · #53C21 #58C40 #58J60 #65J10 #Advanced Neuroimaging Techniques and Applications #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Spectral Theory (math.SP) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2012.09997

openalex publication_date 2020/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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