Spectral convergence of manifold pairs
Abstract
We investigate the spectra of a family of pairs (Mi,Ai) consisting of a complete Riemannian manifold Mi and a closed subset Ai 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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