Minkowski-type and Alexandrov-type theorems for polyhedral herissons

Details Minkowski-type and Alexandrov-type theorems for polyhedral herissons Minkowski-type and Alexandrov-type theorems for polyhedral herissons

2002-11-19

arxiv.org/abs/math/0211286v1

Geom. Dedicata 107, 169-186 (2004)

Mathematics

Metric Geometry

19 pages, 8 figures, LaTeX 2.09

Scientific paper

10.1007/s10711-004-4090-3

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.

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