منابع مشابه
Segments in Ball Packings
Denote by B the n-dimensional unit ball centred at o. It is known that in every lattice packing of B there is a cylindrical hole of infinite length whenever n ≥ 3. As a counterpart, this note mainly proves the following result: For any fixed , > 0, there exist a periodic point set P (n, ) and a constant c(n, ) such that B + P (n, ) is a packing in R, and the length of the longest segment contai...
متن کاملMaximal ball packings of symplectic-toric manifolds
Let (M, σ, ψ) be a symplectic-toric manifold of dimension at least four. This paper investigates the symplectic ball packing problem in the toral equivariant setting. We show that the set of toric symplectic ball packings of M admits the structure of a convex polytope. Previous work of the first author shows that up to equivalence, only (CP)2 and CP admit density one packings when n = 2 and onl...
متن کاملOn Free Planes in Lattice Ball Packings
This note, by studying relations between the length of the shortest lattice vectors and the covering minima of a lattice, mainly proves that for every d-dimensional packing lattice of balls one can find a 4-dimensional plane, parallel to a lattice plane, such that the plane meets none of the balls of the packing, provided the dimension d is large enough. On the other hand, we show that for cert...
متن کاملCombinatorial Scalar Curvature and Rigidity of Ball Packings
Let M be a triangulated three-dimensional manifold. In this paper we define a combinatorial analogue of scalar curvature for M, and also a combinatorial analogue of conformal deformation of the metric. We further define a functional S on the combinatorial conformal deformation space, show that S is concave, and show that critical points of S correspond precisely to metrics of constant combinato...
متن کاملEven More Infinite Ball Packings from Lorentzian Coxeter Systems
Boyd (1974) proposed a class of infinite ball packings that are generated by inversions. Later, Maxwell (1983) interpreted Boyd’s construction in terms of root systems in Lorentz spaces. In particular, he showed that the space-like weight vectors correspond to a ball packing if and only if the associated Coxeter graph is of “level 2”. In Maxwell’s work, the simple roots form a basis of the repr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2001
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-001-0021-3