Antonios Giannopoulos

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Let K be a convex body in R n and let W i (K), i = 1,. .. , n − 1 be its quermassintegrals. We study minimization problems of the form min{W i (T K) | T ∈ SL n } and show that bodies which appear as solutions of such problems satisfy isotropic conditions or even admit an isotropic characterization for appropriate measures. This shows that several well known(More)
It is known that every isotropic convex body K in R n has a " subgaussian " direction with constant r = O(√ log n). This follows from the upper bound |Ψ2(K)| 1/n c √ log n √ n LK for the volume of the body Ψ2(K) with support function h Ψ 2 (K) (θ) := sup 2qn ·,θq √ q. The approach in all the related works does not provide estimates on the measure of(More)