Transplantation and isospectrality. I

DOI10.1007/BF01444635zbMath0735.58008OpenAlexW3025618065MaRDI QIDQ1813033

Pierre H. Bérard

Publication date: 25 June 1992

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164928

zbMATH Keywords

eigenvalue spectrumlength spectrumisospectral manifoldsnon-smooth metricsnatural operatorsSunada's theoremnon-isometric complete non-compact manifolds

Mathematics Subject Classification ID

Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (30)

Isospectral surfaces of genus two and three ⋮ Isoperimetric inequalities for eigenvalues of the Laplacian and the Schrödinger operator ⋮ Linear representations and isospectrality with boundary conditions ⋮ Counting isospectral manifolds ⋮ One cannot hear the shape of a drum ⋮ Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds ⋮ Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups ⋮ Isoscattering on surfaces ⋮ Introduction to some conjectures for spectral minimal partitions ⋮ On the Markovian Similarity ⋮ Determinants of Laplacians and isopolar metrics on surfaces of infinite area. ⋮ Isospectrality and 3-manifold groups ⋮ Small isospectral and nonisometric orbifolds of dimension 2 and 3 ⋮ Spectral decomposition of square-tiled surfaces ⋮ Isospectral Convex Domains in the Hyperbolic Plane ⋮ Isospectral plane domains and surfaces via Riemannian orbifolds ⋮ Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond ⋮ Quantum equivalent magnetic fields that are not classically equivalent ⋮ Isospectrality for spherical space forms ⋮ Intertwining, excursion theory and Krein theory of strings for non-self-adjoint Markov semigroups ⋮ Isoscattering deformations for complete manifolds of negative curvature ⋮ On \(G\)-sets and isospectrality ⋮ Steklov and Robin isospectral manifolds ⋮ Quasi-regular representations of discrete groups and associated $C^*$-algebras ⋮ Isospectrality and Galois projective geometries ⋮ One can't hear orientability of surfaces ⋮ Disjointness-preserving operators and isospectral Laplacians ⋮ Transplantation and Jacobians of Sunada isospectral Riemann surfaces ⋮ Isospectral metrics and potentials on classical compact simple Lie groups ⋮ Continuous families of Riemannian manifolds, isospectral on functions but not on 1-forms

Cites Work

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• Isospectral Riemann surfaces
• Riemannian coverings and isospectral manifolds
• Noncompact Riemannian manifolds with discrete spectra
• Isospectral deformations II: Trace formulas, metrics, and potentials
• Isospectral surfaces of small genus
• Isospectral deformations I: Riemannian structures on two-step nilspaces
• Constructing Isospectral Manifolds
• One cannot hear the shape of a drum

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