Compactness of isospectral sets

Robert Brooks

Displaying similar documents to “Compactness of isospectral sets”

Boundary volume and length spectra of Riemannian manifolds: what the middle degree Hodge spectrum doesn't reveal

Carolyn S. Gordon, Juan Pablo Rossetti (2003)

Annales de l'Institut Fourier

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Let $M$ be a $2 m$ -dimensional compact Riemannian manifold. We show that the spectrum of the Hodge Laplacian acting on $m$ -forms does not determine whether the manifold has boundary, nor does it determine the lengths of the closed geodesics. Among the many examples are a projective space and a hemisphere that have the same Hodge spectrum on 1- forms, and hyperbolic surfaces, mutually isospectral on 1-forms, with different injectivity radii. The Hodge $m$ -spectrum also does not distinguish orbifolds...

Discreteness Conditions for the Laplacian on Complete, Non-Compact Riemannian Manifolds.

Regina Kleine (1988)

Mathematische Zeitschrift

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Continuous families of isospectral metrics on simply connected manifolds.

Schueth, Dorothee (1999)

Annals of Mathematics. Second Series

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Isospectral flat orientable 2-orbifolds.

Isangulov, R.R. (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Curvature and the equivalence problem in sub-Riemannian geometry

Erlend Grong (2022)

Archivum Mathematicum

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These notes give an introduction to the equivalence problem of sub-Riemannian manifolds. We first introduce preliminaries in terms of connections, frame bundles and sub-Riemannian geometry. Then we arrive to the main aim of these notes, which is to give the description of the canonical grading and connection existing on sub-Riemann manifolds with constant symbol. These structures are exactly what is needed in order to determine if two manifolds are isometric. We give three concrete examples,...