2009/03/27 by Grégoire Montcouquiol, Montcouquiol, Grégoire
Computer Science · Mathematics · #52B10 #53C24 #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.DG #msc:52B10 #msc:53C24
paper · pdf · doi:10.48550/arxiv.0903.4743
Final version, accepted for publication in Geom. Dedicata
openalex publication_date 2009/03/27 · arxiv created 2012/10/11 · arxiv updated 2012/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Stoker problem, first formulated in 1968, consists in understanding to what extent a convex polyhedron is determined by its dihedral angles. By means of the double construction, this problem is intimately related to rigidity issues for 3-dimensional cone-manifolds. In a former paper, two such rigidity results were proven, implying that the infinitesimal version of the Stoker conjecture is true in the hyperbolic and Euclidean cases. In this second article, we prove that local rigidity holds and obtain that the space of convex hyperbolic polyhedra with given combinatorial type is locally parameterized by the set of dihedral angles, together with a similar statement for hyperbolic 3-cone-manifolds.