location:  Publications → journals
Search results

Search: MSC category 52A20 ( Convex sets in $n$ dimensions (including convex hypersurfaces) [See also 53A07, 53C45] )

 Expand all        Collapse all Results 1 - 6 of 6

1. CMB 2011 (vol 55 pp. 498)

Fradelizi, Matthieu; Paouris, Grigoris; Schütt, Carsten
 Simplices in the Euclidean Ball We establish some inequalities for the second moment $$\frac{1}{|K|} \int_{K}|x|_2^2 \,dx$$ of a convex body $K$ under various assumptions on the position of $K$. Keywords:convex body, simplexCategory:52A20

2. CMB 2009 (vol 52 pp. 342)

Bezdek, K.; Kiss, Gy.
 On the X-ray Number of Almost Smooth Convex Bodies and of Convex Bodies of Constant Width The X-ray numbers of some classes of convex bodies are investigated. In particular, we give a proof of the X-ray Conjecture as well as of the Illumination Conjecture for almost smooth convex bodies of any dimension and for convex bodies of constant width of dimensions $3$, $4$, $5$ and $6$. Keywords:almost smooth convex body, convex body of constant width, weakly neighbourly antipodal convex polytope, Illumination Conjecture, X-ray number, X-ray ConjectureCategories:52A20, 52A37, 52C17, 52C35

3. CMB 2009 (vol 52 pp. 380)

Henk, Martin; Cifre, Mar\'\i a A. Hernández
 Successive Minima and Radii In this note we present inequalities relating the successive minima of an $o$-symmetric convex body and the successive inner and outer radii of the body. These inequalities join known inequalities involving only either the successive minima or the successive radii. Keywords:successive minima, inner and outer radiiCategories:52A20, 52C07, 52A40, 52A39

4. CMB 2009 (vol 52 pp. 464)

Stancu, Alina
 Two Volume Product Inequalities and Their Applications Let $K \subset {\mathbb{R}}^{n+1}$ be a convex body of class $C^2$ with everywhere positive Gauss curvature. We show that there exists a positive number $\delta (K)$ such that for any $\delta \in (0, \delta(K))$ we have $\Volu(K_{\delta})\cdot \Volu((K_{\delta})^{\sstar}) \geq \Volu(K)\cdot \Volu(K^{\sstar}) \geq \Volu(K^{\delta})\cdot \Volu((K^{\delta})^{\sstar})$, where $K_{\delta}$, $K^{\delta}$ and $K^{\sstar}$ stand for the convex floating body, the illumination body, and the polar of $K$, respectively. We derive a few consequences of these inequalities. Keywords:affine invariants, convex floating bodies, illumination bodiesCategories:52A40, 52A38, 52A20

5. CMB 2004 (vol 47 pp. 246)

Makai, Endre; Martini, Horst
 On Maximal $k$-Sections and Related Common Transversals of Convex Bodies Generalizing results from [MM1] referring to the intersection body $IK$ and the cross-section body $CK$ of a convex body $K \subset \sR^d, \, d \ge 2$, we prove theorems about maximal $k$-sections of convex bodies, $k \in \{1, \dots, d-1\}$, and, simultaneously, statements about common maximal $(d-1)$- and $1$-transversals of families of convex bodies. Categories:52A20, 55Mxx

6. CMB 2002 (vol 45 pp. 232)

Ji, Min; Shen, Zhongmin
 On Strongly Convex Indicatrices in Minkowski Geometry The geometry of indicatrices is the foundation of Minkowski geometry. A strongly convex indicatrix in a vector space is a strongly convex hypersurface. It admits a Riemannian metric and has a distinguished invariant---(Cartan) torsion. We prove the existence of non-trivial strongly convex indicatrices with vanishing mean torsion and discuss the relationship between the mean torsion and the Riemannian curvature tensor for indicatrices of Randers type. Categories:46B20, 53C21, 53A55, 52A20, 53B40, 53A35
 top of page | contact us | privacy | site map |