Random ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces

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dc.creatorKahn, Jeremy
dc.creatorMarkovic, Vladimir
dc.date2008-06-13
dc.date.accessioned2026-07-07T09:44:31Z
dc.date.available2026-07-07T09:44:31Z
dc.descriptionWe prove that any two finite-area non-compact hyperbolic Riemann surfaces S and T have finite covers that are arbitrarily close in the normalized Weil-Petersson metric, where we normalize by dividing the square of the metric by the area of the surface. In the case where T is the modular surface this reduces to showing that S has a finite cover with a proper ideal triangulation where most of the shear coordinates are small; we will construct such a cover out of a random collection of immersed ideal triangles in S.
dc.description86 pages, 4 figures, one three-page flow chart
dc.identifierhttps://arxiv.org/abs/0806.2304
dc.identifierhttp://arxiv.org/abs/0806.2304
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162902
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject30F60, 32G15
dc.titleRandom ideal triangulations and the Weil-Petersson distance between finite degree covers of punctured Riemann surfaces
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