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Geometriae Dedicata

, Volume 107, Issue 1, pp 169–186 | Cite as

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

  • Victor Alexandrov
Article

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.

convex polyhedron polyhedral surface polyhedral hedgehog equipment virtual polytope polygon Cauchy lemma open mapping 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Victor Alexandrov
    • 1
  1. 1.Sobolev Institute of MathematicsRussia.

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