Comptes Rendus
no. 7
Geometry
The reverse Hlawka inequality in a Minkowski space

Presented by: the Editorial Board

Denis Serre1
1 UMPA, UMR CNRS–ENS Lyon # 5669, École normale supérieure de Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 629-633.

We show that in the future cone of the Minkowski space, the pseudo-norm satisfies a Hlawka-type inequality:

ℓ(x)+ℓ(y)+ℓ(z)+ℓ(x+y+z)≤ℓ(x+y)+ℓ(y+z)+ℓ(z+x).
The inequality is opposite to that in the Euclidean case, exactly as in the situation of the Cauchy–Schwarz inequality.

Dans le cône du futur de l'espace de Minkowski, la pseudo-norme associée à la métrique lorentzienne satisfait une inégalité du type de Hlawka :

ℓ(x)+ℓ(y)+ℓ(z)+ℓ(x+y+z)≤ℓ(x+y)+ℓ(y+z)+ℓ(z+x).
Le signe est l'opposé de celui du cas euclidien, tout comme dans l'inégalité « à la Cauchy–Schwarz ».

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.04.008

Denis Serre 1

1 UMPA, UMR CNRS–ENS Lyon # 5669, École normale supérieure de Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, France 
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Denis Serre. The reverse Hlawka inequality in a Minkowski space. Comptes Rendus. Mathématique, Volume 353 (2015) no. 7, pp. 629-633. doi : 10.1016/j.crma.2015.04.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.04.008/

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