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Summary: arXiv:math.MG/0211286
v1
19
Nov
2002 Minkowski-type and Alexandrov-type theorems
for polyhedral herissons
Victor Alexandrov y
November 18, 2002
Abstract
Classical H. Minkowski theorems on existence and uniqueness of con-
vex 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.
Key words: convex polyhedron, polyhedral surface, polyhedral hedge-
hog, equipment, virtual polytope, polygon, Cauchy lemma, open mapping.
2000 Mathematics Subject Classi cation: 52B10, 52C25, 52B70, 52A38,
52A15.
1 Introduction
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