Minimal stretch maps between hyperbolic surfaces

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dc.creatorThurston, William P.
dc.date1998-01-09
dc.date.accessioned2026-07-07T05:23:32Z
dc.date.available2026-07-07T05:23:32Z
dc.descriptionThis paper develops a theory of Lipschitz comparisons of hyperbolic surfaces analogous to the theory of quasi-conformal comparisons. Extremal Lipschitz maps (minimal stretch maps) and geodesics for the `Lipschitz metric' are constructed. The extremal Lipschitz constant equals the maximum ratio of lengths of measured laminations, which is attained with probability one on a simple closed curve. Cataclysms are introduced, generalizing earthquakes by permitting more violent shearing in both directions along a fault. Cataclysms provide useful coordinates for Teichmuller space that are convenient for computing derivatives of geometric function in Teichmuller space and measured lamination space.
dc.description53 pages, 11 figures, version of 1986 preprint
dc.identifierhttps://arxiv.org/abs/math/9801039
dc.identifierhttp://arxiv.org/abs/math/9801039
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/76475
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject57m50
dc.titleMinimal stretch maps between hyperbolic surfaces
dc.typetext

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