Book Review: Geometry of isotropic convex bodies
نویسندگان
چکیده
منابع مشابه
Symmetrization and isotropic constants of convex bodies
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-Min...
متن کاملExtremal Problems and Isotropic Positions of Convex Bodies
Let K be a convex body in R and let Wi(K), i = 1, . . . , n − 1 be its quermassintegrals. We study minimization problems of the form min{Wi(TK) | T ∈ SLn} 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 which play an imp...
متن کاملOn the Isotropic Constant of Non–Symmetric Convex Bodies
We show that Bourgain’s estimate LK ≤ cn 1 4 logn for the isotropic constant holds true for non-symmetric convex bodies as well.
متن کاملMoment inequalities and central limit properties of isotropic convex bodies
Abstract The object of our investigations are isotropic convex bodies , centred at the origin and normed to volume one, in arbitrary dimensions. We show that a certain subset of these bodies—specified by bounds on the second and fourth moments—is invariant under forming ‘expanded joins’. Considering a body as above as a probability space and taking , we define random variables on . It is known ...
متن کاملHigh Dimensional Random Sections of Isotropic Convex Bodies
We study two properties of random high dimensional sections of convex bodies. In the first part of the paper we estimate the central section function |K ∩F⊥| n−k for random F ∈ Gn,k and K ⊂ R n a centrally symmetric isotropic convex body. This partially answers a question raised by V. Milman and A. Pajor (see [MP], p.88). In the second part we show that every symmetric convex body has random hi...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2015
ISSN: 0273-0979,1088-9485
DOI: 10.1090/s0273-0979-2015-01490-4