Electronic Resource
Springer
Acta mathematica hungarica
89 (2000), S. 233-246
ISSN:
1588-2632
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We discuss the concept of the bisector of a segment in a Minkowski normed n-space, and prove that if the unit ball K of the space is strictly convex then all bisectors are topological images of a hyperplane of the embedding Euclidean n-space. The converse statement is not true. We give an example in the three-space showing that all bisectors are topological planes, however K contains segments on its boundary. Strict convexity ensures the normality of Dirichlet-Voronoi-type K-subdivision of any point lattice.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1010611925838
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