Convex polytopes whose projection bodies and difference sets are polars

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Volume difference inequalities for the projection and intersection bodies

In this paper, we introduce a new concept of volumes difference function of the projection and intersection bodies. Following this, we establish the Minkowski and Brunn-Minkowski inequalities for volumes difference function of the projection and intersection bodies.

متن کامل

On Zonoids Whose Polars Are Zonoids

Zonoids whose polars are zonoids, cannot have proper faces other than vertices or facets. However, there exist non–smooth zonoids whose polars are zonoids. Examples in R and R are given.

متن کامل

Random Polytopes, Convex Bodies, and Approximation

Assume K ⊂ R is a convex body and Xn ⊂ K is a random sample of n uniform, independent points from K. The convex hull of Xn is a convex polytope Kn called random polytope inscribed in K. We are going to investigate various properties of this polytope: for instance how well it approximates K, or how many vertices and facets it has. It turns out that Kn is very close to the so called floating body...

متن کامل

Thrifty approximations of convex bodies by polytopes

Given a convex body C ⊂ Rd containing the origin in its interior and a real number τ > 1 we seek to construct a polytope P ⊂ C with as few vertices as possible such that C ⊂ τP . Our construction is nearly optimal for a wide range of d and τ . In particular, we prove that if C = −C then for any 1 > > 0 and τ = 1 + one can choose P having roughly −d/2 vertices and for τ = √ d one can choose P ha...

متن کامل

Fine Approximation of Convex Bodies by Polytopes

We prove that for every convex body K with the center of mass at the origin and every ε ∈ ( 0, 12 ) , there exists a convex polytope P with at most eO(d)ε− d−1 2 vertices such that (1− ε)K ⊂ P ⊂ K.

متن کامل

ذخیره 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: Discrete & Computational Geometry

سال: 1991

ISSN: 0179-5376,1432-0444

DOI: 10.1007/bf02574676