Exceptional directions for a convex body |
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Authors: | B. A. Ivanov |
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Affiliation: | (1) Leningrad Finance-Economics Institute, USSR |
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Abstract: | Let K be a convex body in Rn andO be a point inside K. We examine the Grassmann manifold of k-planes passing throughO. We take as exceptional the planes intersecting K along a body having at least one (k – 1)-dimensional face such that it does not have points inside the hyperfaces of body K. We prove that in the Grassmann manifold Gkn the set of such exceptional planes is of measure zero.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 365–371, September, 1976.The author thanks V. A. Zalgaller for aid and advice on the work. |
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