Optimizing geometric measures for fixed minimal annulus and inradius
The aim of the authors is to investigate all possible and optimal relations stating the maximum and minimum values of the area, perimeter, diameter and the minimal width of a convex body, given its minimal annulus and its inradius. First, optimal upper and lower bounds of the area and perimeter of a convex body are given in terms of its circumradius and inradius. In particular, the case of a convex body with prescribed minimal annulus and inradius is taken into account. In the same manner, optimal upper and lower bounds for the diameter and the minimal width are approached. The corresponding extremal sets are determined for each optimal inequality.
scientific article; zbMATH DE number 5281237