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- W4300908427 abstract "In the Teichmuller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to reparametrization). The lines we construct are special stretch lines in the sense of Thurston. They are directed by complete geodesic laminations that are not chain-recurrent, and they have a nice description in terms of Fenchel-Nielsen coordinates. At the basis of the construction are certain maps with controlled Lipschitz constants between right-angled hyperbolic hexagons having three non-consecutive edges of the same size. Using these maps, we obtain Lipschitz-minimizing maps between hyperbolic particular pairs of pants and, more generally, between some hyperbolic sufaces of finite type with arbitrary genus and arbitrary number of boundary components. The Lipschitz-minimizing maps that we contruct are distinct from Thurston's stretch maps." @default.
- W4300908427 created "2022-10-04" @default.
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- W4300908427 date "2010-01-13" @default.
- W4300908427 modified "2023-10-16" @default.
- W4300908427 title "Some Lipschitz maps between hyperbolic surfaces with applications to Teichmuller theory" @default.
- W4300908427 doi "https://doi.org/10.48550/arxiv.1001.2088" @default.
- W4300908427 hasPublicationYear "2010" @default.
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