The Deformation Space of Geodesic Triangulations and Generalized Tutte's Embedding Theorem
arXiv:2105.00612 · doi:10.2140/gt.2023.27.3361
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.
18 pages, 5 figures. Comments are welcomed!