Quantitative stability in the isodiametric inequality via the isoperimetric inequality

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 ex...

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Bibliographic Details
Published in:	Transactions of the American Mathematical Society Vol. 366; no. 3; pp. 1141 - 1160
Main Authors:	MAGGI, FRANCESCO, PONSIGLIONE, MARCELLO, PRATELLI, ALDO
Format:	Journal Article
Language:	English
Published:	American Mathematical Society 01-03-2014
Subjects:	Isoperimetric problem Mathematical constants Mathematical inequalities Mathematical theorems Polygons Spherical caps Symmetry Unit ball Isodiametric inequality geometric inequalities
Online Access:	Get full text
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Summary:	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.
ISSN:	0002-9947 1088-6850
DOI:	10.1090/S0002-9947-2013-06126-0