Isospectral drums and simple groups

DOI10.1142/S0219887818500603zbMath1386.58018arXiv1507.01968WikidataQ114008511 ScholiaQ114008511MaRDI QIDQ4609889

Koen Thas

Publication date: 26 March 2018

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.01968

zbMATH Keywords

classificationmanifoldexamplessimple groupisospectralitydrumheadGassmann-Sunada tripleirreducible drum

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Wave scattering in solid mechanics (74J20) Gas dynamics (general theory) (76N15) Harmonic analysis on homogeneous spaces (43A85) Hydro- and aero-acoustics (76Q05) Membranes (74K15) Simple groups: alternating groups and groups of Lie type (20D06) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Isospectrality (58J53)

Cites Work

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• Subgroups inducing the same permutation representation
• Riemannian coverings and isospectral manifolds
• Compact isospectral sets of surfaces
• Spectres et groupes cristallographiques. II: Domaines sphériques. (Spectra and crystallographic groups. II: Spherical domains)
• Isospectral and non-isometric Riemannian manifolds
• Isospectral plane domains and surfaces via Riemannian orbifolds
• Linearly equivalent actions of solvable groups
• Permutation characters and fixed-point-free elements in permutation groups.
• Equivalence between isospectrality and isolength spectrality for a certain class of planar billiard domains
• PSL_n(q) as operator group of isospectral drums
• Kac's question, planar isospectral pairs and involutions in projective space: II. Classification of generalized projective isospectral data
• Can One Hear the Shape of a Drum? Revisited
• Compact isospectral sets of plane domains
• On lens spaces which are isospectral but not isometric
• One cannot hear the shape of a drum
• Bounded domains which are isospectral but not congruent
• Some planar isospectral domains
• Finite geometries and diffractive orbits in isospectral billiards
• EIGENVALUES OF THE LAPLACE OPERATOR ON CERTAIN MANIFOLDS
• Length and Eigenvalue Equivalence
• Kac's question, planar isospectral pairs and involutions in projective space
• Can One Hear the Shape of a Drum?

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