Quantitative stability in the isodiametric inequality via the isoperimetric inequality

Details Quantitative stability in the isodiametric inequality via the isoperimetric inequality Quantitative stability in the isodiametric inequality via the isoperimetric inequality

2011-04-20

arxiv.org/abs/1104.4074v1

Mathematics

Metric Geometry

Scientific paper

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.

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