Quantitative stability in the isodiametric inequality via the isoperimetric inequality

Maggi, Francesco; Ponsiglione, Marcello; Pratelli, Aldo

doi:10.1090/S0002-9947-2013-06126-0

Quantitative stability in the isodiametric inequality via the isoperimetric inequality
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by Francesco Maggi, Marcello Ponsiglione and Aldo Pratelli PDF

Trans. Amer. Math. Soc. 366 (2014), 1141-1160 Request permission

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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