Optimizing geometric measures for fixed minimal annulus and inradius

Abstract

In this paper we relate the minimal annulus of a planar convex body $K$ with its inradius, obtaining all the upper and lower bounds, in terms of these quantities, for the classic geometric measures associated with the set: area, perimeter, diameter, minimal width and circumradius. We prove the optimal inequalities for each one of those problems, determining also its corresponding extremal sets.