scholarly journals The Projections of Convex Lattice Sets of Points in E2

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Yu Gu ◽  
Lin Si
Keyword(s):  
Discrete Version ◽  
Symmetric Convex ◽  
Projection Theorem ◽  
Lattice Polygon ◽  
Convex Lattice ◽  
Centrally Symmetric

Can one determine a centrally symmetric lattice polygon by its projections? In 2005, Gardner et al. proposed the above discrete version of Aleksandrov’s projection theorem. In this paper, we define a coordinate matrix for a centrally symmetric convex lattice set and suggest an algorithm to study this problem.

scholarly journals A measure of axial symmetry of centrally symmetric convex bodies

2010 ◽  
Vol 121 (2) ◽  
pp. 295-306 ◽  
Author(s):  
Marek Lassak ◽  
Monika Nowicka
Keyword(s):  
Axial Symmetry ◽  
Convex Bodies ◽  
Symmetric Convex ◽  
Centrally Symmetric

A characterization of centrally symmetric convex bodies in En

1981 ◽  
Vol 10 (1-4) ◽  
pp. 161-176 ◽  
Author(s):  
D. G. Larman ◽  
N. K. Tamvakis
Keyword(s):  
Convex Bodies ◽  
Symmetric Convex ◽  
Centrally Symmetric

Some problems concerning centrally symmetric convex bodies

1978 ◽  
Vol 10 (3) ◽  
pp. 454-460
Author(s):  
V. A. Zalgaller ◽  
V. N. Sudakov
Keyword(s):  
Convex Bodies ◽  
Symmetric Convex ◽  
Centrally Symmetric

scholarly journals Centrally symmetric convex bodies and sections having maximal quermassintegrals

2012 ◽  
Vol 49 (2) ◽  
pp. 189-199
Author(s):  
E. Makai ◽  
H. Martini
Keyword(s):  
Convex Body ◽  
Convex Bodies ◽  
The Body ◽  
Symmetric Convex ◽  
Local Theorem ◽  
Centrally Symmetric ◽  
Euclidean Unit Ball ◽  
Analogous Theorem ◽  
Lower Dimensional ◽  
Dimensional Surface

Let d ≧ 2, and let K ⊂ ℝd be a convex body containing the origin 0 in its interior. In a previous paper we have proved the following. The body K is 0-symmetric if and only if the following holds. For each ω ∈ Sd−1, we have that the (d − 1)-volume of the intersection of K and an arbitrary hyperplane, with normal ω, attains its maximum if the hyperplane contains 0. An analogous theorem, for 1-dimensional sections and 1-volumes, has been proved long ago by Hammer (see [2]). In this paper we deal with the ((d − 2)-dimensional) surface area, or with lower dimensional quermassintegrals of these intersections, and prove an analogous, but local theorem, for small C2-perturbations, or C3-perturbations of the Euclidean unit ball, respectively.

scholarly journals Self-packing of centrally symmetric convex bodies in ℝ2

1992 ◽  
Vol 8 (2) ◽  
pp. 171-189 ◽  
Author(s):  
P. G. Doyle ◽  
J. C. Lagarias ◽  
D. Randall
Keyword(s):  
Convex Bodies ◽  
Symmetric Convex ◽  
Centrally Symmetric
Sign in / Sign up

Export Citation Format

Share Document