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See detailBending laminations on convex hulls of anti-de Sitter quasicircles
merlin, louis; Schlenker, Jean-Marc UL

in Proceedings of the London Mathematical Society (in press)

Let λ− and λ+ be two bounded measured laminations on the hyperbolic disk H2, which "strongly fill" (definition below). We consider the left earthquakes along λ− and λ+, considered as maps from the ... [more ▼]

Let λ− and λ+ be two bounded measured laminations on the hyperbolic disk H2, which "strongly fill" (definition below). We consider the left earthquakes along λ− and λ+, considered as maps from the universal Teichmüller space T to itself, and we prove that the composition of those left earthquakes has a fixed point. The proof uses anti-de Sitter geometry. Given a quasi-symmetric homeomorphism u:RP1→RP1, the boundary of the convex hull in AdS3 of its graph in RP1×RP1≃∂AdS3 is the disjoint union of two embedded copies of the hyperbolic plane, pleated along measured geodesic laminations. Our main result is that any pair of bounded measured laminations that "strongly fill" can be obtained in this manner. [less ▲]

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See detailEquations of hyperelliptic Shimura curves
Molina Blanco, Santiago UL

in Proceedings of the London Mathematical Society (2012), 105(5), 891--920

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See detailFive torsion points on curves of genus two
Boxall, John; Grant, David; Leprévost, Franck UL

in Proceedings of the London Mathematical Society (2000)

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