Volume Inequalities and Additive Maps of Convex Bodies
نویسندگان
چکیده
منابع مشابه
Volume Inequalities and Additive Maps of Convex Bodies
Analogs of the classical inequalities from the Brunn Minkowski Theory for rotation intertwining additive maps of convex bodies are developed. We also prove analogs of inequalities from the dual Brunn Minkowski Theory for intertwining additive maps of star bodies. These inequalities provide generalizations of results for projection and intersection bodies. As a corollary we obtain a new Brunn Mi...
متن کاملVolume 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 کاملVolume Inequalities for Sets Associated with Convex Bodies
This paper deals with inequalities for the volume of a convex body and the volume of the projection body, the L-centroid body, and their polars. Examples are the Blaschke-Santaló inequality, the Petty and Zhang projection inequalities, the Busemann-Petty inequality. Other inequalities of the same type are still at the stage of conjectures. The use of special continuous movements of convex bodie...
متن کاملvolume 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 کاملApproximating the Volume of Convex Bodies
It is a well known fact that for every polynomial time algorithm which gives an upper bound V (K) and a lower bound V (K) for the volume of a convex set K ⊂ E, the ratio V (K)/V (K) is at least (cd/ log d). Here we describe an algorithm which gives for ǫ > 0 in polynomial time an upper and lower bound with the property V (K)/V (K) ≤ d!(1 + ǫ).
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ژورنال
عنوان ژورنال: Mathematika
سال: 2006
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579300000103