Isospectral Riemann surfaces

1986/01/01 by Peter Buser · 3 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Finite Group Theory Research #Isospectral #Riemann surface #Laplace operator #Mathematics #Isometric exercise #Spectrum (functional analysis) #Pure mathematics #Construct (python library) #Riemann hypothesis #Algebra over a field #Mathematical analysis #Physics #Computer science #Quantum mechanics

paper · pdf · doi:10.5802/aif.1054

openalex publication_date 1986/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> and for all <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> . In a second part we give examples of isospectral non isometric surfaces in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi mathvariant="bold">R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> which are realizable by paper models.

Citations

• Eigenvalues in Riemannian Geometry
• The eigenvalue spectrum as moduli for compact Riemann surfaces
• Riemannian Coverings and Isospectral Manifolds
• Selberg's trace formula as applied to a compact riemann surface
• The Length Spectra as Moduli for Compact Riemann Surfaces

Cited by

• Some planar isospectral domains
• Isospectral plane domains and surfaces via Riemannian orbifolds
• Isospectral [wikipedia]