## Eigenvalues In Spectral Gaps Of A Perturbed Periodic Manifold (2001)

by
Olaf Post

Citations: | 3 - 2 self |

### BibTeX

@MISC{Post01eigenvaluesin,

author = {Olaf Post},

title = {Eigenvalues In Spectral Gaps Of A Perturbed Periodic Manifold},

year = {2001}

}

### OpenURL

### Abstract

We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the number of eigenvalue branches crossing a fixed level is established in terms of a discrete eigenvalue problem. Furthermore, we discuss examples of perturbations leading to infinitely many eigenvalue branches coming from above resp.