Affine Isoperimetric Inequalities for $L_p$-Intersection Bodies
نویسندگان
چکیده
منابع مشابه
Lp AFFINE ISOPERIMETRIC INEQUALITIES
Affine isoperimetric inequalities compare functionals, associated with convex (or more general) bodies, whose ratios are invariant under GL(n)-transformations of the bodies. These isoperimetric inequalities are more powerful than their better-known relatives of a Euclidean flavor. To be a bit more specific, this article deals with inequalities for centroid and projection bodies. Centroid bodies...
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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.
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Corresponding to each convex (or more general) subset of n-dimensional Euclidean space, Rn, there is a unique ellipsoid with the following property. The moment of inertia of the ellipsoid and the moment of inertia of the convex set are the same about every 1-dimensional subspace of Rn. This ellipsoid is called the Legendre ellipsoid of the convex set. The Legendre ellipsoid is a well-known conc...
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We consider affine analogues of the isoperimetric inequality in the sense of piecewise linear (PL) manifolds. Given a closed polygon P having n edges, embedded in R, we give upper and lower bounds for the minimal number of triangles t needed to form a triangulated PL surface embedded in R having P as its geometric boundary. More generally we obtain such bounds for a triangulated (locally flat) ...
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.
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2010
ISSN: 0035-7596
DOI: 10.1216/rmj-2010-40-2-489