Bisectors in Minkowski 3-Space
Ákos G. Horváth · 2002
We discuss the concept of the bisector of a segment in a Minkowski normed n-space. We prove that all bisectors are topological images of a plane of the embedding Euclidean 3-space iff the shadow boundaries of the unit ball K are topological circles. To a conjectured proving strategy for dimensions n, we introduce the concept of general parameter sphere of the unit ball K, corresponding to a direction vector of the n-space and to a positive parameter. We prove that the Haussdorff limit of these ”spheres ” is the shadow boundary of K of the same direction.