Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps
Periodic Manifolds, Spectral Gaps, and Eigenvalues in Gaps
We investigate spectral properties of the Laplace operator on a class of non-compact Riemannian manifolds. We prove that for a given number N we can construct a periodic manifold such that the essential spectrum of the corresponding Laplacian has at least N open gaps. Furthermore, by perturbing the periodic metric …