02-308 Olaf Post

Periodic Manifolds with Spectral Gaps (132K, LaTeX2e with 3 PS-Figures) Jul 14, 02

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Abstract. 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.

Files: 02-308.src( 02-308.keywords , gaps.tex , figure-1.eps , figure-2.eps , figure-3.eps )