2006/04/18 by A. Epstein, Adam Epstein, V. Markovic +5
Mathematics · #37F30 #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.DS #msc:37F30
paper · pdf · doi:10.48550/arxiv.math/0604411
LaTeX, 15 pages
arxiv created 2006/04/18 · openalex publication_date 2006/04/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We show that the set of points in the Teichmuller space of the universal hyperbolic solenoid which do not have a Teichmuller extremal representative is generic (that is, its complement is the set of the first kind in the sense of Baire). This is in sharp contrast with the Teichmuller space of a Riemann surface where at least an open, dense subset has Teichmuller extremal representatives. In addition, we provide a sufficient criteria for the existence of Teichmuller extremal representatives in the given homotopy class. These results indicate that there is an interesting theory of extremal (and uniquely extremal) quasiconformal mappings on hyperbolic solenoids.