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arXiv · 2204.08145

The convergence of inversive distance circle packings to the Riemann mapping

Yuxiang Chen·Yanwen Luo·Xu Xu
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Abstract

Bowers and Stephenson introduced the notion of inversive distance circle packings as a natural generalization of Thurston's circle packings. They further conjectured that discrete conformal maps induced by inversive distance circle packings converge to the Riemann mapping. In this paper, we prove Bowers-Stephenson's conjecture for Jordan domains by establishing a solvability theorem of certain prescribing combinatorial curvature problems for inversive distance circle packings.

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Yuxiang Chen, Yanwen Luo, Xu Xu. 2022-04-18. The convergence of inversive distance circle packings to the Riemann mapping. https://arxiv.org/abs/2204.08145

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