Symmetrization and isotropic constants of convex bodies
نویسنده
چکیده
We investigate the effect of a Steiner type symmetrization on the isotropic constant of a convex body. We reduce the problem of bounding the isotropic constant of an arbitrary convex body, to the problem of bounding the isotropic constant of a finite volume ratio body. We also add two observations concerning the slicing problem. The first is the equivalence of the problem to a reverse Brunn-Minkowski inequality in isotropic position. The second is the essential monotonicity in n of Ln = supK⊂Rn LK where the supremum is taken over all convex bodies in R, and LK is the isotropic constant of K.
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