The length of closed geodesics on random Riemann Surfaces

dc.creatorMakover, Eran
dc.creatorMcGowan, Jeffrey
dc.date2005-04-08
dc.date.accessioned2026-07-07T05:18:55Z
dc.date.available2026-07-07T05:18:55Z
dc.descriptionShort geodesics are important in the study of the geometry and the spectra of Riemann surfaces. Bers' theorem gives a global bound on the length of the first $3g-3$ geodesics. We use the construction of Brooks and Makover of random Riemann surfaces to investigate the distribution of short ($< \log (g)$) geodesics on a random Riemann surfaces. We calculate the expected value of the shortest geodesic, and show that if one orders prime non-intersecting geodesics by length $γ_1\le γ_2\le ... \le γ_i ,...$, then for fixed $k$, if one allows the genus to go to infinity, the length of $γ_{k}$ is independent of the genus.
dc.description6 figures
dc.identifierhttps://arxiv.org/abs/math/0504175
dc.identifierhttp://arxiv.org/abs/math/0504175
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74836
dc.subjectDifferential Geometry
dc.subjectMetric Geometry
dc.subject58J50
dc.titleThe length of closed geodesics on random Riemann Surfaces
dc.typetext

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