G. Averkov, A. Heppes: Constant Minkowskian width in terms of boundary cuts

Author(s):

Gennadiy Averkov
Aladar Heppes

Title:

Constant Minkowskian width in terms of boundary cuts

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 6, 2004

Abstract:

Let $K$ be a body of constant width in a Minkowski space (i.e., a finite dimensional real Banach space) with unit ball $B$. Suppose that $B$ and $K$ are strictly convex and smooth. Then any manifold $M_0$, homeomorphic to $(d-2)$-simensional sphere and lying in the boundary bd $K$ of $K$ splits bd $K$ into two compact manifolds $M_1$ and $M_2$ such that $M_1$ or $M_2$ has the same Minkowskian diameter as $M_0$. Moreover, the above property of bodies having constant Minkowskian width is even characteristic in the class of strictly convex and smooth bodies with at least two Minkowskian diametral chords.

Keywords:

constant width, Minkowski space, Banach space

Language:

English

Publication time:

2004