 05244 Lled\'o, Fernando and Post, Olaf
 Generating spectral gaps by geometry
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Jul 15, 05

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Abstract. Motivated by the analysis of Schr\"odinger operators with periodic potentials we consider the following abstract situation: Let $\Delta_X$ be the Laplacian on a noncompact Riemannian covering manifold $X$ with a discrete isometric group $\Gamma$ acting on it such that the quotient $X/\Gamma$ is a compact manifold. We prove the existence of a finite number of spectral gaps for the operator $\Delta_X$ associated with a suitable class of manifolds $X$ with nonabelian covering transformation groups $\Gamma$. This result is based on the nonabelian Floquet theory as well as the MinMaxprinciple. Groups of type I specify a class of examples satisfying the assumptions of the main theorem.
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