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hal-00692820, version 1

THE CONVEX INTERSECTION BODY OF A CONVEX BODY

Mathieu Meyer 1, Shlomo Reisner

Glasgow Mathematical Journal 53, ? (2011) 523--534

Abstract: Let L be a convex body in R(n) and z an interior point of L. We associate with L and z a new, convex and centrally symmetric, body CI(L, z). This generalizes the classical intersection body I(L, z) (whose radial function at u is an element of S(n-1) is the volume of the hyperplane section of L through z, orthogonal to u). CI(L, z) coincides with I(L, z) if and only if L is centrally symmetric about z. We study the properties of CI(L, z).

  • 1:  Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA)
  • Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout
  • Domain : Mathematics/Mathematical Physics
 
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  • http://hal-upec-upem.archives-ouvertes.fr/hal-00692820
  • oai:hal-upec-upem.archives-ouvertes.fr:hal-00692820
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  • Submitted on: Tuesday, 1 May 2012 13:38:23
  • Updated on: Tuesday, 1 May 2012 13:38:31