Bending laminations on convex hulls of anti-de Sitter quasicircles
| Autor: | Jean-Marc Schlenker, Louis Merlin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Mathematics::Dynamical Systems 010308 nuclear & particles physics General Mathematics 010102 general mathematics Regular polygon Geometric Topology (math.GT) Geometry Bending 01 natural sciences Mathematics::Geometric Topology quasicircle Mathematics - Geometric Topology bending lamination Differential Geometry (math.DG) Hull 0103 physical sciences FOS: Mathematics Mathematics [G03] [Physical chemical mathematical & earth Sciences] Anti-de Sitter space Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre] 0101 mathematics convex hull Mathematics |
| Popis: | Let $\lambda_-$ and $\lambda_+$ be two bounded measured laminations on the hyperbolic disk $\mathbb H^2$, which "strongly fill" (definition below). We consider the left earthquakes along $\lambda_-$ and $\lambda_+$, considered as maps from the universal Teichm\"uller space $\mathcal T$ 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 $u:{\mathbb RP}^1\to {\mathbb RP}^1$, the boundary of the convex hull in $AdS^3$ of its graph in ${\mathbb RP}^1\times{\mathbb RP}^1\simeq \partial AdS^3$ 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. Comment: 16 pages |
| Databáze: | OpenAIRE |
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