The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem

Yanwen Luo; Tianqi Wu; Xiaoping Zhu

doi:10.2140/gt.2023.27.3361

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arXiv · 2105.00612

The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem

Yanwen Luo·Tianqi Wu·Xiaoping Zhu

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Abstract

We proved the contractibility of the deformation space of the geodesic triangulations on a closed surface of negative curvature. This solves an open problem proposed by Connelly et al. in 1983, in the case of hyperbolic surfaces. The main part of the proof is a generalization of Tutte's embedding theorem for closed surfaces of negative curvature.

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Yanwen Luo, Tianqi Wu, Xiaoping Zhu. 2021-05-03. The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem. https://doi.org/10.2140/gt.2023.27.3361

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