Spectral convergence of manifold pairs

Details Spectral convergence of manifold pairs Spectral convergence of manifold pairs

2002-09-05

arxiv.org/abs/math/0209051v2

Mathematics

Differential Geometry

31 pages, no figures, Lemma 2.2 corrected

Scientific paper

We investigate the spectra of a family of pairs (M_i,A_i) consisting of a complete Riemannian manifold M_i and a closed subset A_i and which converge in the Lipschitz topology to a pair (M,A). This is used to construct manifolds of bounded curvature, nonempty essential spectrum, infinitely many eigenvalues below the essential spectrum and with an arbitrary number of such eigenvlues of arbitrarily high multiplicity.

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