Zone diagrams in compact subsets of uniformly convex normed spaces
نویسندگان
چکیده
منابع مشابه
Zone diagrams in compact subsets of uniformly convex normed spaces
A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matoušek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and...
متن کاملExistence of zone diagrams in compact subsets of uniformly convex spaces
A zone diagram is a relatively new concept which has emerged in computational geometry and is related to Voronoi diagrams. Formally, it is a fixed point of a certain mapping, and neither its uniqueness nor its existence are obvious in advance. It has been studied by several authors, starting with T. Asano, J. Matoušek and T. Tokuyama, who considered the Euclidean plane with singleton sites, and...
متن کاملThe geometric stability of Voronoi diagrams in normed spaces which are not uniformly convex
The Voronoi diagram is a geometric object which is widely used in many areas. Recently it has been shown that under mild conditions Voronoi diagrams have a certain continuity property: small perturbations of the sites yield small perturbations in the shapes of the corresponding Voronoi cells. However, this result is based on the assumption that the ambient normed space is uniformly convex. Unfo...
متن کاملPorosity of Convex Nowhere Dense Subsets of Normed Linear Spaces
and Applied Analysis 3 Definition 2.4. M is called c-porous if for any x ∈ X and every r > 0, there are y ∈ B x, r and φ ∈ X∗ \ {0} such that { z ∈ X : φ z > φy ∩M ∅. 2.2 C-porosity turns out to be the suitable notion to describe the smallness of convex nowhere dense sets see Proposition 2.5 and is a stronger form of 0-angle porosity x ∈ X instead x ∈ M . Indeed, consider the unit sphere S of a...
متن کاملSome Uniformly Convex Spaces
size of the éliminants but the size of their largest prime factor which is important, and secondly it is not essential to take the w's in order of magnitude. In answer, it should be pointed out that after one passes the limits of factor tables, it becomes impracticable to deal with the factors of the éliminant rather than the éliminant. Therefore, since the éliminant (in one case at least) appe...
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: Israel Journal of Mathematics
سال: 2011
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-011-0094-5