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Comptes Rendus Mathématique
Volume 353, n° 7
pages 629-633 (juillet 2015)
Doi : 10.1016/j.crma.2015.04.008
Received : 21 October 2014 ;  accepted : 14 April 2015
The reverse Hlawka inequality in a Minkowski space
L'inégalité de Hlawka inverse dans un espace de Minkowski
 

Denis Serre
 UMPA, UMR CNRS–ENS Lyon # 5669, École normale supérieure de Lyon, 46, allée d'Italie, 69364 Lyon cedex 07, France 

Abstract

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.

The full text of this article is available in PDF format.
Résumé

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 ».

The full text of this article is available in PDF format.


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