Cages of small length holding convex bodies

Augustin Fruchard (1) , Tudor Zamfirescu (2)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
2 IMAR - Institut de Mathématiques de l'Académie Roumaine

A cage G, defined as the 1-skeleton of a convex polytope, holds a compact set K disjoint from G, if K cannot be moved away without intersecting G. The main results of this paper establish the minimal length of cages holding various compact convex sets. First, planar graphs and Steiner trees are investigated. Then the notion of " almost fixing points " for planar convex bodies is introduced and studied. The last two sections treat cages holding 2-dimensional, respectively 3-dimensional, compact convex sets.

Mots clés: Immobilisation; skeleton; Steiner tree; convex body

Domaines: Géométrie métrique [math.MG]

Augustin Fruchard, Tudor Zamfirescu. Cages of small length holding convex bodies. 2017. ⟨hal-01573138⟩