DCG
2007
13 years 4 months ago
2007
DCG
2007
13 years 5 months ago
2007
Let C be a cone in R3 whose base B is a planar convex body in a horizontal plane π and whose tip is a point v /∈ π. Let C be a packing formed by translates of C and −C in R3...
DCG
2007
13 years 5 months ago
2007
We study two notions. One is that of spindle convexity. A set of circumradius not greater than one is spindle convex if, for any pair of its points, it contains every short circula...
DCG
2007
13 years 5 months ago
2007
DCG
2007
13 years 5 months ago
2007
We extend to topological affine planes the standard theorems of convexity, among them the separation theorem, the anti-exchange theorem, Radon’s, Helly’s, Carath´eodory’s,...
DCG
2007
13 years 5 months ago
2007
Scalar functions defined on a topological space Ω are at the core of many applications such as shape matching, visualization and physical simulations. Topological persistence i...
DCG
2007
13 years 5 months ago
2007
Any finite set X ⊂ Rd colored with d+3 2 colors, contains a rainbow subset Y ⊂ X, such that any ball that contains Y contains a positive fraction of the points of X. The bound...
DCG
2007
13 years 5 months ago
2007
It is proved that the shape of the typical cell of a stationary and isotropic Poisson random hyperplane tessellation is, with high probability, close to the shape of a ball if the ...
DCG
2007
13 years 5 months ago
2007
The aim of this paper is to initiate the study of alcoved polytopes, which are polytopes arising from affine Coxeter arrangements. This class of convex polytopes includes many clas...
DCG
2007
13 years 5 months ago
2007