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Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

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.

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Alexandrov, V. Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons. Geometriae Dedicata 107, 169–186 (2004). https://doi.org/10.1007/s10711-004-4090-3

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  • DOI: https://doi.org/10.1007/s10711-004-4090-3

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