Optimizing the perimeter and the area of convex sets with fixed diameter and circumradius
The author determines planar convex sets which have minimum area or perimeter when the diameter and the circumradius are prescribed, obtaining the corresponding geometric inequalities. She uses these inequalities to obtain two complete systems of inequalities: systems of inequalities relating all the geometric characteristics such that, for any set of numbers satisfying those conditions, a planar figure with these values of the characteristics exists. She obtains the corresponding Blaschke's diagrams for these complete systems. Such results give a complete answer to two questions posed by Santalo in 1961.
scientific article; zbMATH DE number 1837418
scientific article