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arXiv · 2507.17466

On the spectral stability of finite coverings

Werner Ballmann·Sugata Mondal·Panagiotis Polymerakis
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Abstract

We prove the non-existence of new eigenvalues in $[0,\Lambda]$ for specific and random finite coverings of a complete and connected Riemannian manifold $M$ with Ricci curvature bounded from below, where $\Lambda$ is any positive number below the essential spectrum of $M$ and the spectrum of the universal cover of $M$, provided the representation theory of the fundamental group of $M$ satisfies certain conditions.

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Werner Ballmann, Sugata Mondal, Panagiotis Polymerakis. 2025-07-23. On the spectral stability of finite coverings. https://arxiv.org/abs/2507.17466

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