«intersection body»
۲۵۵۹ نتیجهvolume 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.
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.
Inequalities for dual quermassintegrals of mixed intersection bodies
In this paper, we first introduce a new concept of dual quermassintegral sum function of two star bodies and establish Minkowski's type inequality for dual quermassintegral sum of mixed intersection bodies, which is a general form of the Minkowski inequality for mixed intersectio
On the local convexity of intersection bodies of revolution
One of the fundamental results regarding intersection bodies is Busemann’s theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is natural to ask how much of convexity is guaranteed under the intersection body operation. In this paper we
Isomorphic Properties of Intersection Bodies
We study isomorphic properties of two generalizations of intersection bodies the class I k of k-intersection bodies in R and the class BPk of generalized k-intersection bodies in R. In particular, we show that all convex bodies can be in a certain sense approximated by intersecti
Intersection Bodies and Generalized Cosine Transforms
Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. We review some known facts and give them new proofs. The main focus is in
The unit ball is an attractor of the intersection body operator
The intersection body of a ball is again a ball. So, the unit ball Bd ⊂Rd is a fixed point of the intersection body operator acting on the space of all star-shaped origin symmetric bodies endowed with the Banach– Mazur distance. E. Lutwak asked if there is any other star-shaped b
Lp-dual geominimal surface areas for the general Lp-intersection bodies
For 0 < p < 1, Haberl and Ludwig defined the notions of symmetric and asymmetric Lp-intersection bodies. Recently, Wang and Li introduced the general Lp-intersection bodies. In this paper, we give the Lp-dual geominimal surface area forms for the extremum values and Brunn-Minkows
COUNTEREXAMPLES TO CONVEXITY OF k-INTERSECTION BODIES
It is a well-known result due to Busemann that the intersection body of an origin-symmetric convex body is also convex. Koldobsky introduced the notion of k-intersection bodies. We show that the k-intersection body of an origin-symmetric convex body is not necessarily convex if k
Non-intersection Bodies All of Whose Central Sections Are Intersection Bodies
We construct symmetric convex bodies that are not intersection bodies, but all of their central hyperplane sections are intersection bodies. This result extends the studies by Weil in the case of zonoids and by Neyman in the case of subspaces of Lp.