The Length Spectrum of a Riemann Surface is Always of Unbounded Multiplicity

DOI10.2307/2042345zbMath0447.30034OpenAlexW4242091736MaRDI QIDQ3892503

Burton Randol

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/2042345

zbMATH Keywords

Riemann surfacelength spectrum

Mathematics Subject Classification ID

Compact Riemann surfaces and uniformization (30F10) Geodesics in global differential geometry (53C22)

Related Items (16)

On small gaps in the length spectrum ⋮ Stable degeneracies for Ising models ⋮ Length spectra of the Hecke triangle groups ⋮ The Sunada construction and the simple length spectrum ⋮ Degeneracy in the length spectrum for metric graphs ⋮ Prising apart geodesics by length in hyperbolic manifolds ⋮ Free energy as a dynamical invariant (or can you hear the shape of a potential?) ⋮ Horowitz-Randol pairs of curves in \(q\)-differential metrics ⋮ On equivalence of simple closed curves in flat surfaces ⋮ Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space ⋮ Constructing metrics on a 2-torus with a partially prescribed stable norm ⋮ Stable multiplicities in the length spectrum of Riemann surfaces ⋮ Geometry of Riemann surfaces based on closed geodesics ⋮ Translation equivalence in free groups ⋮ Length muliplicities of hyperbolic 3-manifolds ⋮ Correlations for pairs of closed geodesics

Cites Work

• Some inverse spectral results for negatively curved 2-manifolds
• Characters of free groups represented in the two‐dimensional special linear group
• On Dehn's algorithms for the conjugacy and word problems, with applications

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