Calculus of Variations and Geometric Measure Theory
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F. Maggi - M. Ponsiglione - A. Pratelli

Quantitative stability in the isodiametric inequality via the isoperimetric inequality

created by ponsiglio on 20 Apr 2011
modified by maggi on 13 Jul 2020


Published Paper

Inserted: 20 apr 2011
Last Updated: 13 jul 2020

Journal: Trans. AMS
Year: 2011


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


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