Minkowski-type and Alexandrov-type theorems for polyhedral herissons
arXiv:math/0211286 · doi:10.1007/s10711-004-4090-3
Abstract
Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.
19 pages, 8 figures, LaTeX 2.09