Periodic Manifolds with Spectral Gaps

Details Periodic Manifolds with Spectral Gaps Periodic Manifolds with Spectral Gaps

2002-07-14

arxiv.org/abs/math-ph/0207017v1

Physics

Mathematical Physics

21 pages, 3 eps-figures, LaTeX

Scientific paper

We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. For a given number $N$ we construct periodic (i.e. covering) manifolds such that the essential spectrum of the corresponding Laplacian has at least $N$ open gaps. We use two different methods. First, we construct a periodic manifold starting from an infinite number of copies of a compact manifold, connected by small cylinders. In the second construction we begin with a periodic manifold which will be conformally deformed. In both constructions, a decoupling of the different period cells is responsible for the gaps.

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