Discretization of vector bundles and rough Laplacian

2006/09/21 by Tatiana Mantuano, Mantuano, Tatiana · 1 citation
Mathematics · #53C20 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #math.DG #math.SP #msc:53C20 #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0609595

arxiv created 2006/09/21 · arxiv updated 2009/12/01

Abstract

We establish a uniform comparison between the spectrum of the rough Laplacian (acting on sections of a vector bundle of complex rank one or of harmonic curvature) with the spectrum of a discrete operator (a generalization of a discrete magnetic Laplacian added with a potential) acting on a finite dimensional space coming from a discretization process. As an application, we obtain a comparison of the first positive eigenvalue of the rough Laplacian with the holonomy.

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• Eigenvalue Estimate for the Rough Laplacian on 1-Forms and its Applications

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