Reference : Bending laminations on convex hulls of anti-de Sitter quasicircles
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
Bending laminations on convex hulls of anti-de Sitter quasicircles
merlin, louis []
Schlenker, Jean-Marc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > >]
Proceedings of the London Mathematical Society
Oxford University Press
Yes (verified by ORBilu)
United Kingdom
[en] convex hull ; quasicircle ; bending lamination
[en] 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.

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