Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495923 | Journal of Functional Analysis | 2005 | 23 Pages |
Abstract
Here we show that any centrally-symmetric convex body KâRn has a perturbation TâRn which is convex and centrally-symmetric, such that the isotropic constant of T is universally bounded. T is close to K in the sense that the Banach-Mazur distance between T and K is O(logn). If K is a body of a non-trivial type then the distance is universally bounded. The distance is also universally bounded if the perturbation T is allowed to be non-convex. Our technique involves the use of mixed volumes and Alexandrov-Fenchel inequalities. Some additional applications of this technique are presented here.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
B. Klartag,