On the Volume Ratio of Two Convex Bodies |
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| Authors: | Giannopoulos, A. Hartzoulaki, M. |
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| Affiliation: | Department of Mathematics, University of Crete Iraklion, Greece. giannop{at}fourier.math.uoc.gr
Department of Mathematics, University of Crete Iraklion, Greece hmarian{at}math.uch.gr |
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| Abstract: | Let K and L be two convex bodies in Rn. The volume ratio vr(K,L) of K and L is defined by vr(K, L = inf(|K|/|T(L)|)1/n, wherethe infimum is over all affine transformations T of Rn for whichT(L)  K. It is shown in this paper that vr(K, L)   , where c > 0 is an absolute constant. This isoptimal up to the logarithmic term. 2000 Mathematics SubjectClassification 52A40, 46B07 (primary); 52A21, 52A20 (secondary). |
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