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Rapid Steiner Symmetrization of Most of a Convex Body and the Slicing Problem

2005
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Combinatorics, probability & computing
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For an arbitrary n-dimensional convex body, at least almost n Steiner symmetrizations are required in order to symmetrize the body into an isomorphic ellipsoid. We say that a body T ⊂ R n is "quickly symmetrizable" if for any ε > 0 there exist only εn symmetrizations that transform T into a body which is c(ε)-isomorphic to an ellipsoid, where c(ε) depends solely on ε. In this note we ask, given a body K ⊂ R n , whether it is possible to remove a small portion of its volume and obtain a body T ⊂

doi:10.1017/s0963548305006899
fatcat:bttnnordtra3tkjhezf2jm6cxi