Eigenvalues in spectral gaps of a perturbed periodic manifold | Zendy

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Eigenvalues in spectral gaps of a perturbed periodic manifold

Author(s) -

Post Olaf

Publication year - 2003

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200310117

Subject(s) - mathematics , eigenvalues and eigenvectors , spectral gap , manifold (fluid mechanics) , riemannian manifold , metric (unit) , laplace operator , upper and lower bounds , pure mathematics , mathematical analysis , quantum mechanics , physics , mechanical engineering , operations management , engineering , economics

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)

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