Mutually isospectral Riemann surfaces

DOI10.1006/aima.1998.1750zbMath0997.53031OpenAlexW2079364632MaRDI QIDQ1272795

Ruth Gornet, Robert Brooks, William H. Gustafson

Publication date: 7 March 1999

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/f1cc0ef3b1b49404aca90fe4d473c2ac7fcc2f62

zbMATH Keywords

Riemann surfacesnumber fieldsgraphsspectrum of Laplacian

Mathematics Subject Classification ID

Other number fields (11R21) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Harmonic functions on Riemann surfaces (30F15)

Related Items (16)

Counting isospectral manifolds ⋮ Sunada transplantation and isogeny of intermediate Jacobians of compact Kähler manifolds ⋮ Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups ⋮ Interrogating surface length spectra and quantifying isospectrality ⋮ Determinants of Laplacians and isopolar metrics on surfaces of infinite area. ⋮ Zeta functions that hear the shape of a Riemann surface ⋮ A large family of cospectral Cayley graphs over dicyclic groups ⋮ \({\mathbb{Z}}_2^k\)-manifolds are isospectral on forms ⋮ Families of mutually isospectral Riemannian orbifolds ⋮ Quantum equivalent magnetic fields that are not classically equivalent ⋮ Spectral rigidity and discreteness of 2233-groups ⋮ Steklov and Robin isospectral manifolds ⋮ Non-Sunada graphs ⋮ Transplantation and Jacobians of Sunada isospectral Riemann surfaces ⋮ Isospectral metrics and potentials on classical compact simple Lie groups ⋮ Isospectral deformations of negatively curved Riemannian manifolds with boundary which are not locally isometric.

Cites Work

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• Isospectral deformations of compact solvmanifolds
• Riemannian coverings and isospectral manifolds
• Isospectral and non-isometric Riemannian manifolds
• Recent results in the theory of graph spectra
• On the equation \(\zeta_K(s)=\zeta_{K'}(s)\)
• Non-Sunada graphs
• Isospectral deformations I: Riemannian structures on two-step nilspaces
• Maximal Fuchsian groups
• Geometry and spectra of compact Riemann surfaces

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