On the isotropy constant of random convex sets
نویسندگان
چکیده
منابع مشابه
About the Isotropy Constant of Random Convex Sets
K 〈x, θ〉2dx = LK ∀θ ∈ Sn−1 where LK is a constant independent of θ, which is called the isotropy constant of K. Here 〈·, ·〉 denotes the standard scalar product in R. It is well known that for every convex body K ∈ R there exists an affine map T such that TK is isotropic. Furthermore, K and TK are both isotropic if and only if T is an orthogonal transformation. In this case the isotropy constant...
متن کاملConvex sets of constant width
A bounded convex set has constant width d iff any two parallel (and nonidentical) tangent planes to it have identical distance d from each other. Clearly balls have this property, but there are also other sets of constant width. This lecture was originally designed for a general audience as part of a series of lectures during the German “Year of Mathematics” 2008. It starts by presenting eviden...
متن کاملConvex Sets of Constant Width and -diameter
PETER HÄSTÖ, ZAIR IBRAGIMOV AND DAVID MINDA ABSTRACT. In this article we study -diameter of planar sets of constant width. We obtain analogues of the isodiametric inequality and the Blaschke-Lebesgue Theorem for -diameter of constant width sets. Namely, we prove that among all the sets of given constant width, disks have the smallest -diameter and Reuleaux triangles have the largest -diameter. ...
متن کاملOn the Isotropy Constant of Projections of Polytopes
The isotropy constant of any d-dimensional polytope with n vertices is bounded by C p n/d where C > 0 is a numerical constant.
متن کاملOn the hyperplane conjecture for random convex sets
This seemingly innocuous question, considered two decades ago by Bourgain [3, 4], has not been answered yet. We refer the reader to, e.g., [2], [18] or [14] for partial results, history and for additional literature regarding this hyperplane conjecture. In particular, there are large classes of convex bodies for which an affirmative answer to the above question is known. These include unconditi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09487-2