Some characterisations of the ellipsoid |
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Authors: | G R Burton |
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Institution: | (1) Mathematics Department, University College London, Gower Street, WC1E 6BT London, England |
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Abstract: | We show that a convex bodyK of dimensiond≧3 is an ellipsoid if it has any of the following properties: (1) the “grazes” of all points close toK are flat, (2) all sections of small diameter are centrally symmetric, (3) parallel (d−1)-sections close to the boundary are width-equivalent, (4)K is strictly convex and all (d−1)-sections close to the boundary are centrally symmetric; the last two results are deduced from their 3-dimensional cases
which were proved by Aitchison. |
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