One more proof of the Alexandrov–Fenchel inequality

Dario Cordero-Erausquin; Bo'az Klartag; Quentin Merigot; Filippo Santambrogio

doi:10.1016/j.crma.2019.07.004

Functional analysis/Geometry

One more proof of the Alexandrov–Fenchel inequality

Presented by: Gilles Pisier

Dario Cordero-Erausquin ¹; Bo'az Klartag ²; Quentin Merigot ³; Filippo Santambrogio 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

Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 676-680.

Abstract
Résumé

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

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.

Received: 2019-04-18
Accepted: 2019-07-16
Published online: 2019-08-01

DOI: 10.1016/j.crma.2019.07.004

Author's affiliations:

Dario Cordero-Erausquin ¹; Bo'az Klartag ²; Quentin Merigot ³; Filippo Santambrogio 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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     author = {Dario Cordero-Erausquin and Bo'az Klartag and Quentin Merigot and Filippo Santambrogio},
     title = {One more proof of the {Alexandrov{\textendash}Fenchel} inequality},
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     pages = {676--680},
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Dario Cordero-Erausquin; Bo'az Klartag; Quentin Merigot; Filippo Santambrogio. One more proof of the Alexandrov–Fenchel inequality. Comptes Rendus. Mathématique, Volume 357 (2019) no. 8, pp. 676-680. doi : 10.1016/j.crma.2019.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.07.004/

References
Cited by

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