Quantitative Isoperimetric Inequalities on the Real Line

Abstract : In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown that, in the Gauss space, a set of given measure and almost minimal Gauss boundary measure is necessarily close to be a half-space. Using only geometric tools, we extend their result to all symmetric log-concave measures \mu on the real line. We give sharp quantitative isoperimetric inequalities and prove that among sets of given measure and given asymmetry (distance to half line, i.e. distance to sets of minimal perimeter), the intervals or complements of intervals have minimal perimeter.
Type de document :
Article dans une revue
Annales mathématiques Blaise Pascal, cedram, 2011, 18 (2), pp.251-271
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https://hal.inria.fr/inria-00579987
Contributeur : Yohann De Castro <>
Soumis le : mercredi 30 janvier 2013 - 13:25:26
Dernière modification le : jeudi 18 janvier 2018 - 10:39:12

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  • HAL Id : inria-00579987, version 1
  • ARXIV : 1011.3995

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Yohann De Castro. Quantitative Isoperimetric Inequalities on the Real Line. Annales mathématiques Blaise Pascal, cedram, 2011, 18 (2), pp.251-271. 〈inria-00579987〉

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