The metric geometry of paper surfaces under geometric constraints
Metric Geometry
2026-02-12 v1 Algebraic Topology
Dynamical Systems
General Topology
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.
Keywords
Cite
@article{arxiv.2602.10826,
title = {The metric geometry of paper surfaces under geometric constraints},
author = {Luciana Menezes Vasconcelos},
journal= {arXiv preprint arXiv:2602.10826},
year = {2026}
}