Immobilization of convex bodies in {mathbb {R}}^n

Abstract

We extend to arbitrary finite n the notion of immobilization of a convex body O in {mathbb {R}}^n by a finite set of points {mathcal {P}} in the boundary of O. Because of its importance for this problem, necessary and sufficient conditions are found for the immobilization of an n-simplex. A fairly complete geometric description of these conditions is given: as n increases from n = 2, some qualitative difference in the nature of the sets {mathcal {P}} emerges.