JournalsaihpcVol. 26, No. 6pp. 2511–2519

A refined Brunn–Minkowski inequality for convex sets

  • A. Figalli

    Laboratoire de Mathématiques Laurent Schwartz, École Polytechnique, F-91128 Palaiseau cedex, France

  • F. Maggi

    Università di Firenze, Dipartimento di Matematica, viale Morgagni 67/A, 50134 Firenze, Italy

  • A. Pratelli

    Università di Pavia, Dipartimento di Matematica, Via Ferrata 1, 27100 Pavia, Italy
A refined Brunn–Minkowski inequality for convex sets cover
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Abstract

Starting from a mass transportation proof of the Brunn–Minkowski inequality on convex sets, we improve the inequality showing a sharp estimate about the stability property of optimal sets. This is based on a Poincaré-type trace inequality on convex sets that is also proved in sharp form.

Cite this article

A. Figalli, F. Maggi, A. Pratelli, A refined Brunn–Minkowski inequality for convex sets. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, pp. 2511–2519

DOI 10.1016/J.ANIHPC.2009.07.004