Quantitative stability in the isodiametric inequality via the isoperimetric inequality
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- by Francesco Maggi, Marcello Ponsiglione and Aldo Pratelli PDF
- Trans. Amer. Math. Soc. 366 (2014), 1141-1160 Request permission
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.References
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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
- MR Author ID: 685324
- Email: ponsigli@mat.uniroma1.it
- Aldo Pratelli
- Affiliation: Department Mathematik, Universität Erlangen-Nürnberg, Cauerstrasse 11, 91058 Erlangen, Germany
- Email: pratelli@math.fau.de
- Received by editor(s): April 26, 2011
- Published electronically: November 21, 2013
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 1141-1160
- MSC (2010): Primary 51N20
- DOI: https://doi.org/10.1090/S0002-9947-2013-06126-0
- MathSciNet review: 3145725