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THE CONVEX INTERSECTION BODY OF A CONVEX BODY

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).
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Submitted on : Tuesday, May 1, 2012 - 1:38:23 PM
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Mathieu Meyer, Shlomo Reisner. THE CONVEX INTERSECTION BODY OF A CONVEX BODY. Glasgow Mathematical Journal, Cambridge University Press (CUP), 2011, 53 (?), pp.523--534. ⟨10.1017/S0017089511000103⟩. ⟨hal-00692820⟩

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