The isodiametric inequality is derived from the isoperimetric inequality through a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter. This principle also brings quantitative improvements to the isodiametric inequality, shown to be sharp by explicit nearly optimal sets.
Quantitative stability in the isodiametric inequality via the isoperimetric inequality / Francesco Maggi; Marcello Ponsiglione; Aldo Pratelli. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 366:(2014), pp. 1141-1160. [10.1090/S0002-9947-2013-06126-0]
Quantitative stability in the isodiametric inequality via the isoperimetric inequality
MAGGI, FRANCESCO;
2014
Abstract
The isodiametric inequality is derived from the isoperimetric inequality through a variational principle, establishing that balls maximize the perimeter among convex sets with fixed diameter. This principle also brings quantitative improvements to the isodiametric inequality, shown to be sharp by explicit nearly optimal sets.
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