no. 8
Functional analysis/Geometry
One more proof of the Alexandrov–Fenchel inequality
[Une autre preuve de l'inégalité d'Alexandrov–Fenchel]

Présenté par : Gilles Pisier

Cordero-Erausquin, Dario1 ; Klartag, Bo'az2 ; Merigot, Quentin3 ; Santambrogio, Filippo4
1 Institut de mathématiques de Jussieu, Sorbonne Université, 4, place Jussieu, 75252 Paris cedex 05, France
2 Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
3 Laboratoire de mathématiques d'Orsay, Universié Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
4 Institut Camille-Jordan, Université Claude-Bernard – Lyon-1, 43, boulevard du 11-Novembre-1918, 69622 Villeurbanne cedex, France
Comptes Rendus. Mathématique, Tome 357 (2019) no. 8, pp. 676-680.

Nous donnons une preuve courte des inégalités d'Alexandrov–Fenchel qui repose sur des propriétés algébriques élémentaires ou de convexité des volumes mixtes de polytopes.

We present a short proof of the Alexandrov–Fenchel inequalities, which mixes elementary algebraic properties and convexity properties of mixed volumes of polytopes.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2019.07.004
Cordero-Erausquin, Dario 1 ; Klartag, Bo'az 2 ; Merigot, Quentin 3 ; Santambrogio, Filippo 4

1 Institut de mathématiques de Jussieu, Sorbonne Université, 4, place Jussieu, 75252 Paris cedex 05, France
2 Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
3 Laboratoire de mathématiques d'Orsay, Universié Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France
4 Institut Camille-Jordan, Université Claude-Bernard – Lyon-1, 43, boulevard du 11-Novembre-1918, 69622 Villeurbanne cedex, France 
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     title = {One more proof of the {Alexandrov{\textendash}Fenchel} inequality},
     journal = {Comptes Rendus. Math\'ematique},
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Cordero-Erausquin, Dario; Klartag, Bo'az; Merigot, Quentin; Santambrogio, Filippo. One more proof of the Alexandrov–Fenchel inequality. Comptes Rendus. Mathématique, Tome 357 (2019) no. 8, pp. 676-680. doi : 10.1016/j.crma.2019.07.004. http://www.numdam.org/articles/10.1016/j.crma.2019.07.004/

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