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 06 Sep 2013

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Inserted: 20 apr 2011
Last Updated: 6 sep 2013

Year: 2011

Abstract:

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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