Eigenvalues in spectral gaps of a perturbed periodic manifold

✍ Scribed by Olaf Post

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 325 KB
• Volume: 261-262
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310117

✦ Synopsis

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. finitely many branches coming from below. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)