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Quantitative stability in the isodiametric inequality via the isoperimetric inequality


Authors: Francesco Maggi, Marcello Ponsiglione and Aldo Pratelli
Journal: Trans. Amer. Math. Soc. 366 (2014), 1141-1160
MSC (2010): Primary 51N20
DOI: https://doi.org/10.1090/S0002-9947-2013-06126-0
Published electronically: November 21, 2013
MathSciNet review: 3145725
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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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Additional Information

Francesco Maggi
Affiliation: Department of Mathematica, The University of Texas at Austin, RLM 8.100 2515 Speedway Stop C1200, Austin, Texas 78712-1202
Email: maggi@math.utexas.edu

Marcello Ponsiglione
Affiliation: Dipartmento di Matematics, “G. Castelnuovo”, “Sapienza Università di Roma”, P.le Aldo Moro 5, I-00185 Roma, Italy
Email: ponsigli@mat.uniroma1.it

Aldo Pratelli
Affiliation: Department Mathematik, Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany
Email: pratelli@math.fau.de

DOI: https://doi.org/10.1090/S0002-9947-2013-06126-0
Keywords: Isodiametric inequality, geometric inequalities
Received by editor(s): April 26, 2011
Published electronically: November 21, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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