Antonios Giannopoulos

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Let K be a convex body in R n and let be its quermassintegrals. We study minimization problems of the form minfW i (TK) j T 2 SL n g 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 positions of convex bodies(More)
We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If K is a convex body in R n with volume one and center of mass at the origin, there exists x = 0 such that |{y ∈ K : |y, x| t·, x1}| exp(−ct 2 / log 2 (t + 1)) for all t 1, where c > 0 is an absolute constant. The proof is(More)
Let K be a symmetric convex body in R n. It is well-known that for every θ ∈ (0, 1) there exists a subspace F of R n with dim F = [(1 − θ)n] such that where P F denotes the orthogonal projection onto F. Consider a fixed coordinate system in R n. We study the question whether an analogue of (*) can be obtained when one is restricted to choose F among the(More)