Eigenvalues In Spectral Gaps Of A Perturbed Periodic Manifold

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

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by Olaf Post

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2 - 2 self

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@MISC{Post01eigenvaluesin,
    author = {Olaf Post},
    title = {Eigenvalues In Spectral Gaps Of A Perturbed Periodic Manifold},
    year = {2001}
}

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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.

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