The metric geometry of paper surfaces under geometric constraints
Abstract
We investigate the quasisymmetric uniformization of a special class of metric surfaces known as paper surfaces, constructed as quotients of planar multipolygons via segment pairings, including infinite Type W identifications. These spaces, which arise naturally in dynamical settings, exhibit conic singularities and complex geometric structure. Our goal is to prove that a broad class of such surfaces satisfies Ahlfors 2-regularity and linear local contractibility, which together ensure the existence of a quasisymmetric parametrization onto the standard 2-sphere.
Fields of Study & Subjects
Analytic and geometric function theory
Geometric Analysis and Curvature Flows
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Annales Fennici Mathematici
- Volume
- 51
- Issue
- 2
- Pages
- 741–778
- Publication date
- 21 October 2026
- Language
- EN