| Approximation of Convex Bodies by ConvexBodies |
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| 引用本文： | 国起,StenKaijser. Approximation of Convex Bodies by ConvexBodies[J]. 东北数学, 2003, 0(4) |
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| 作者姓名： | 国起 StenKaijser |
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| 作者单位： | Department of Mathematics，Uppsala University，Box 480，S-751 06 Uppsala，Sweden，Department of Mathematics，Uppsala University，Box 480，S-751 06 Uppsala，Sweden |
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| 摘 要： | For the affine distance d(C,D) between two convex bodies C, D(?) Rn, which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C, D) have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C, D) < n1/2 if one is an ellipsoid and another is symmetric, d(C, D) < n if both are symmetric, and from F. John's result and d(C1,C2) < d(C1,C3)d(C2,C3) one has d(C,D) < n2 for general convex bodies; M. Lassak proved d(C, D) < (2n - 1) if one of them is symmetric. In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies.
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Approximation of Convex Bodies by ConvexBodies |
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| GUO Qi and Sten Kaijser. Approximation of Convex Bodies by ConvexBodies[J]. Northeastern Mathematical Journal, 2003, 0(4) |
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| Authors: | GUO Qi and Sten Kaijser |
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| Abstract: | For the affine distance d(C,D) between two convex bodies C, D(?) Rn, which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C, D) have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C, D) < n1/2 if one is an ellipsoid and another is symmetric, d(C, D) < n if both are symmetric, and from F. John's result and d(C1,C2) < d(C1,C3)d(C2,C3) one has d(C,D) < n2 for general convex bodies; M. Lassak proved d(C, D) < (2n - 1) if one of them is symmetric. In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies. |
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| Keywords: | convex body measure of asymmetry Banach-Mazur distance |
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