Relating the minimal annulus with the circumradius of a convex set

Abstract

In this paper we relate the minimal annulus of a planar convex body K with its circumradius, obtaining all the upper and lower bounds, in terms of these quantities, for some of the classic geometric measures associated with the set: the diameter, the minimal width and the inradius. We prove the optimal inequalities for each one of those problems, determining also its corresponding extremal sets. Mathematics subject classification (2010): 52A40, 52A10, 52A38.