Miquel Sätze in Minkowski-Ebenen I.
Some examples of affine planes non-extensible to a Laguerre plane are studied and conditions for the uniqueness of a Laguerre extension are given.
Let be a Minkowski space with a unit ball and let be the Hausdorff metric induced by in the hyperspace of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of which can be joined by unique metric segments with respect to for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace over any two-dimensional Minkowski space.