Approximation of Convex Bodies by Centrally Symmetric Bodies |
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Authors: | Marek Lassak |
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Institution: | (1) Instytut Matematyki i Fizyki ATR, 85-796 Bydgoszcz, Poland; e-mail |
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Abstract: | We present an analog of the well-known theorem of F. John about the ellipsoid of maximal volume contained in a convex body. Let C be a convex body and let D be a centrally symmetric convex body in the Euclidean d-space. We prove that if D is an affine image of D of maximal possible volume contained in C, then C a subset of the homothetic copy of D with the ratio 2d-1 and the homothety center in the center of D . The ratio 2d-1 cannot be lessened as a simple example shows. |
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Keywords: | convex body approximation affine transformation volume Banach– Mazur distance |
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