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Compactness of \(D\)-isospectral metrics. (English) Zbl 1167.58017
The author generalizes, to the case of Schrödinger operators \(D\), some compactness results on the spaces of isospectral metrics as well as results of finiteness of diffeomorphism types of isospectral manifolds. In dimension 3, under lower bounds on the Ricci curvature, he gives a result of compactness modulo gauge equivalence of isospectral metrics on a given manifold. In dimensions other than 4, he shows that certain classes of isospectral manifolds (relatively to a family of Schrödinger operators) satisfying lower bounds on the sectional curvatures contain finitely many types of diffeomorphisms.

MSC:
58J53 Isospectrality
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