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Search: MSC category 58J53 ( Isospectrality )

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1. CMB 2013 (vol 57 pp. 357)

Lauret, Emilio A.
 Representation Equivalent Bieberbach Groups and Strongly Isospectral Flat Manifolds Let \$\Gamma_1\$ and \$\Gamma_2\$ be Bieberbach groups contained in the full isometry group \$G\$ of \$\mathbb{R}^n\$. We prove that if the compact flat manifolds \$\Gamma_1\backslash\mathbb{R}^n\$ and \$\Gamma_2\backslash\mathbb{R}^n\$ are strongly isospectral then the Bieberbach groups \$\Gamma_1\$ and \$\Gamma_2\$ are representation equivalent, that is, the right regular representations \$L^2(\Gamma_1\backslash G)\$ and \$L^2(\Gamma_2\backslash G)\$ are unitarily equivalent. Keywords:representation equivalent, strongly isospectrality, compact flat manifoldsCategories:58J53, 22D10

2. CMB 2010 (vol 53 pp. 684)

Proctor, Emily; Stanhope, Elizabeth
 An Isospectral Deformation on an Infranil-Orbifold We construct a Laplace isospectral deformation of metrics on an orbifold quotient of a nilmanifold. Each orbifold in the deformation contains singular points with order two isotropy. Isospectrality is obtained by modifying a generalization of Sunada's theorem due to DeTurck and Gordon. Keywords:spectral geometry, global Riemannian geometry, orbifold, nilmanifoldCategories:58J53, 53C20

3. CMB 2009 (vol 52 pp. 66)

Dryden, Emily B.; Strohmaier, Alexander
 Huber's Theorem for Hyperbolic Orbisurfaces We show that for compact orientable hyperbolic orbisurfaces, the Laplace spectrum determines the length spectrum as well as the number of singular points of a given order. The converse also holds, giving a full generalization of Huber's theorem to the setting of compact orientable hyperbolic orbisurfaces. Keywords:Huber's theorem, length spectrum, isospectral, orbisurfacesCategories:58J53, 11F72

4. CMB 2006 (vol 49 pp. 226)

Engman, Martin
 The Spectrum and Isometric Embeddings of Surfaces of Revolution A sharp upper bound on the first \$S^{1}\$ invariant eigenvalue of the Laplacian for \$S^1\$ invariant metrics on \$S^2\$ is used to find obstructions to the existence of \$S^1\$ equivariant isometric embeddings of such metrics in \$(\R^3,\can)\$. As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in \$(\R^3,\can)\$. This leads to generalizations of some classical results in the theory of surfaces. Categories:58J50, 58J53, 53C20, 35P15