Thurston's boundary to infinite-dimensional Teichmüller spaces: geodesic currents

2015/05/05 by Dragomir Šarić, Saric, Dragomir
Mathematics · #30F60 #32G15 #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1505.01099

openalex publication_date 2015/05/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let X₀ be a complete borderless infinite area hyperbolic surface. We introduce Thurston's boundary to the Teichmüller space T(X₀) of the surface X₀ using Liouville (geodesic) currents. Thurston's boundary to T(X₀) is identified with the space PML_bdd(X₀) of projective bounded measured laminations on X₀ which naturally extends Thurston's result for closed surfaces. Moreover, the quasiconformal mapping class group MCG_qc(X₀) acts continuously on the closure T(X₀)∪ PML_bdd(X₀).

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