The geometry and spectrum of the one holed torus

DOI10.1007/BF02566766zbMath0649.53028MaRDI QIDQ1105845

K.-D. Semmler, Peter Buser

Publication date: 1988

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/140121

zbMATH Keywords

Riemann surfacesLaplacianlength spectrumgeodesic boundarymoduli problemisospectral surfaces

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Geodesics in global differential geometry (53C22) Structure of modular groups and generalizations; arithmetic groups (11F06) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Classification theory of Riemann surfaces (30F20)

Related Items (14)

Iso-length-spectral problem for complete hyperbolic surfaces of finite type ⋮ On the rigidity of triangle groups \((r,p,q)\). ⋮ Closed curves and geodesics with two self-intersections on the punctured torus ⋮ On systoles and ortho spectrum rigidity ⋮ Enumerating palindromes and primitives in rank two free groups. ⋮ Determinants of Laplacians and isopolar metrics on surfaces of infinite area. ⋮ Geometric determination of the systole of triangle groups ⋮ Multiplicities of simple closed geodesics and hypersurfaces in Teichmüller space ⋮ Minimal length of two intersecting simple closed geodesics ⋮ Distribution of Resonances for Hyperbolic Surfaces ⋮ Trace coordinates of Teichmüller space of Riemann surfaces of signature (0,4) ⋮ Spectral rigidity and discreteness of 2233-groups ⋮ The triangle groups \((2,p,q)\) are characterized by their length spectrum. ⋮ The modular torus has maximal length spectrum

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