Isospectral hyperbolic surfaces have matching geodesics

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dc.creatorDoyle, Peter G.
dc.creatorRossetti, Juan Pablo
dc.date2006-05-30
dc.date2009-04-08
dc.date.accessioned2026-07-07T13:01:24Z
dc.date.available2026-07-07T13:01:24Z
dc.descriptionWe show that if two closed hyperbolic surfaces (not necessarily orientable or even connected) have the same Laplace spectrum, then for every length they have the same number of orientation-preserving geodesics and the same number of orientation-reversing geodesics. Restricted to orientable surfaces, this result reduces to Huber's theorem of 1959. Appropriately generalized, it extends to hyperbolic 2-orbifolds (possibly disconnected). We give examples showing that it fails for disconnected flat 2-orbifolds.
dc.descriptionVersion dated 29 April 2008; GNU FDL
dc.identifierhttps://arxiv.org/abs/math/0605765
dc.identifierhttp://arxiv.org/abs/math/0605765
dc.identifierNew York J. Math. 14 (2008) 193-2004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226136
dc.subjectDifferential Geometry
dc.subjectSpectral Theory
dc.subject58J53
dc.titleIsospectral hyperbolic surfaces have matching geodesics
dc.typetext

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