Averkov, Gennadiy : Constant Minkowskian width in terms of double normals
- Author(s):
-
Averkov, Gennadiy
- Title:
- Constant Minkowskian width in terms of double normals
- Preprint series:
- Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2002
- Mathematics Subject Classification:
-
52A21 [ Finite-dimensional Banach spaces ] 52A38 [ Length, area, volume ] 52A10 [ Convex sets in $2$ dimensions ] 52A20 [ Convex sets in $n$ dimensions ] - Abstract:
- We extend the notion of a double normal of a convex body from smooth strictly convex Minkowski spaces to arbitrary real, normed, linear spaces in two different ways. Then for both of the ways we obtain the following characterization theorem: a convex body $K$ in a Minkowski plane is of constant Minkowskian width iff every chord $I$ of $K$ splits it into two compact convex sets $K_1$ and $K_2,$ such that $I$ is a Minkowskian double normal of $K_1$ or $K_2.$ Furthermore, this theorem applied to the Euclidean plane is extended to $d$-dimensional Euclidean spaces.
- Keywords:
- body of constant (Minkowskian) width, Minkowski space, double normal, section, hyperplane
- Language:
-
English
- Publication time:
- 12 / 2002
