The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem
Geometric Topology
2023-11-22 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2105.00612,
title = {The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem},
author = {Yanwen Luo and Tianqi Wu and Xiaoping Zhu},
journal= {arXiv preprint arXiv:2105.00612},
year = {2023}
}
Comments
18 pages, 5 figures. Comments are welcomed!