Year: 2026
Type: preprint
Abstract: The main result of the paper shows that each connected polyhedral surface with a hyperbolic background metric, or a Euclidean background metric with uniformly bounded circumdisk radii, is discrete conformal to a complete constant-curvature Riemannian surface equipped with a nonempty closed discrete subset. We also prove a discrete Riemann mapping theorem. The proofs are based on the recent work on the discrete Schwarz lemma, the discrete Liouville theorem for polyhedral surfaces, and a Weyl-type realization theorem for hyperbolic surfaces.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204193207