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The slices of a cone and a characterization of ellipsoids

Abstract : Let C be a convex cone in R-d with non-empty interior and a compact basis K. If H-1 and H-2 are any two parallel hyperplanes tangent to K, whose slices with C are two other compact basis K-1 and K-2, let D, D-1 and D-2 be the truncated subcones of C generated by K, K-1 and K-2.(.) We prove that K is an ellipsoid if, and only if, vol (D)(2) = vol (D-1) vol (D-2) for every such pair of hyperplanes H-1 and H-2.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00693899
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Submitted on : Thursday, May 3, 2012 - 9:15:22 AM
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  • HAL Id : hal-00693899, version 1

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Mathieu Meyer, M Rogalski. The slices of a cone and a characterization of ellipsoids. Mathematika, University College London, 1998, 45 (90), pp.305--317. ⟨hal-00693899⟩

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