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arXiv · 2602.10826

The metric geometry of paper surfaces under geometric constraints

Luciana Menezes Vasconcelos
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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.

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Luciana Menezes Vasconcelos. 2026-02-11. The metric geometry of paper surfaces under geometric constraints. https://arxiv.org/abs/2602.10826

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