Affiliation:
1. Department of Mathematics, University Carlos III Madrid, Avda. de la Universidad 30, E-28911 Leganes (Madrid), Spain
2. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, D-12489 Berlin, Germany
Abstract
In the present paper we consider Riemannian coverings (X,g) → (M,g) with residually finite covering group Γ and compact base space (M,g). In particular, we give two general procedures resulting in a family of deformed coverings (X,gε) → (M,gε) such that the spectrum of the Laplacian Δ(Xε,gε) has at least a prescribed finite number of spectral gaps provided ε is small enough. If Γ has a positive Kadison constant, then we can apply results by Brüning and Sunada to deduce that spec Δ(X,gε) has, in addition, band-structure and there is an asymptotic estimate for the number [Formula: see text] of components of spec Δ(X,gε) that intersect the interval [0,λ]. We also present several classes of examples of residually finite groups that fit with our construction and study their interrelations. Finally, we mention several possible applications for our results.
Publisher
World Scientific Pub Co Pte Lt
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Reference53 articles.
1. On the Spectrum of Periodic Schrödinger Operators and a Tower of Coverings
2. T. Adachi, T. Sunada and P. W. Sy, Analyse Algébrique des Perturbations Singulières, II (Marseille-Luminy, 1991), Travaux en Cours 48 (Hermann, Paris, 1994) pp. 125–133.
3. Large gaps in point-coupled periodic systems of manifolds
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