Spectral instability of coverings

2023/11/24 by Mondal, Sugata, Ballmann, Werner · 2 citations
#35P15 #53C20 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2311.14445

Abstract

We study the behaviour of eigenvalues, below the bottom of the essential spectrum, of the Laplacian under finite Riemannian coverings of complete and connected Riemannian manifolds. We define spectral stability and instability of such coverings. Among others, we provide necessary conditions for stability or, equivalently, sufficient conditions for instability.

Cited by

• On the spectral stability of finite coverings
• Spectral gap of random covers of negatively curved noncompact surfaces

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