Work

Bending laminations on convex hulls of anti‐de Sitter quasi‐circles

Year: 2021

Type: article

Abstract: 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 A⁢d⁢S3 of its graph in RP1×RP1≃∂A⁢d⁢S3 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.

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.12401

Authors: Louis Merlin, Jean‐Marc Schlenker

Institutions: RWTH Aachen University, University of Luxembourg

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Fonds National de la Recherche Luxembourg, Fonds De La Recherche Scientifique - FNRS, RWTH Aachen University

Awards: RNMS: Geometric structures and representation varieties, G2154494988, RNMS: Geometric Structures and Representation Varieties, G8288644858, RNMS: Geometric Structures and Representation Varieties