2009/01/01 by Curtis T. McMullen · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Geometry and complex manifolds #Ribbon #Holomorphic function #Mathematics #Unit disk #Moduli space #Limiting #Unit (ring theory) #Plane (geometry) #Tree (set theory) #Pure mathematics #Moduli #Geometry #Mathematical analysis #Combinatorics #Physics
paper · doi:10.1112/jtopol/jtn032
openalex publication_date 2009/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Let Δ ⊂ ℂ denote the unit disk, viewed as a model for the hyperbolic plane. Under rescaling, Δ takes on the appearance of a tree, with an additional ribbon structure coming from the cyclic ordering of its ends. In this paper, we show that branched coverings of ribbon trees naturally compactify the space of proper holomorphic maps f : (Δ, 0) → (Δ, 0), and use the structure of these ribbon trees to describe the limiting moduli of f.