Inserted: 20 apr 2011
Last Updated: 13 jul 2020
Journal: Trans. AMS
The isodiametric inequality is derived from the isoperimetric inequality trough a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter. This principle brings also quantitative improvements to the isodiametric inequality, shown to be sharp by explicit nearly optimal sets.
Keywords: Geometric inequalities