The first interpretation is related to the strong slicing conjecture, which suggests that for any convex body K ⊆ Rn,. LK ≤ L∆n = (n!) 1 n. (n + 1) n+1. 2n.
In order to obtain this inequality, sharp inclusion results between the convex bodies in this family are obtained whenever $g$ satisfies a better type of ...
In this paper, we obtain the best possible value of the absolute constant C such that for every isotropic convex body K ⊆ R n the following inequality ...
Milman (1984) Brunn theorem and a concentration of volume phenomenon for symmetric convex bodies, G AFA Seminar Notes, Tel Aviv. University. Google Scholar.
Apr 10, 2022 · We prove that Bourgain's hyperplane conjecture and the Kannan-Lovász-Simonovits. (KLS) isoperimetric conjecture hold true up to a factor that is ...
Abstract. Here we show that any centrally-symmetric convex body K ⊂ Rn has a perturbation T ⊂ Rn which is convex and centrally-symmetric,.
Over the last decade or so, quite a lot of effort has been expended on the so-called slicing problem in convex geometry, which asks whether there is a.
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Jun 22, 2022 · Abstract:In 1957, Hadwiger conjectured that every convex body in \mathbb{R}^d can be covered by 2^d translates of its interior.
Apr 20, 2021 · ... convex sets and, moreover, it was shown to imply Bourgain's slicing conjecture. Very recently, Yuansi Chen obtained a striking breakthrough ...
Theorem 1. Let Q be a centro-symmetric convex body in RN with volume U and diagonal covariance matrix (V28¡f), 1 < i,j < N. Let P be a K-dimensional vector.
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