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Comptes Rendus Mathématique
Volume 352, n° 3
pages 245-249 (mars 2014)
Doi : 10.1016/j.crma.2013.12.013
Received : 22 October 2013 ;  accepted : 16 December 2013
Majorations asymptotiques du barycentre convexe d'une mesure de probabilité sur les espaces homogènes  ,   et l'espace de Heisenberg  
Asymptotic upper bounds for the convex barycenter of probability measure on the homogenous spaces  ,   and the Heisenberg space  
 

Mohamed Gorine , Mohamed Belkhelfa
 L.P.Q. 3M, faculté des sciences et de la technologie, université de Mascara, Algérie 

Résumé

On supposera donnée une mesure de probabilité μ portée par un petit compact dans une variété différentiable M . Notre but est de trouver des majorations du barycentre convexe de μ lorsque M est l'un des espaces homogènes  ,   ou l'espace de Heisenberg  . Les majorations sont obtenues par construction de fonctions convexes presque affines.

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

Assume given a probability measure μ carried on a small compact in a differentiable manifold M . Our goal is to find upper bounds for the convex barycenter of μ where M is one of the spaces  ,   or the Heisenberg space  . The upper bounds are obtained with the construction of almost affine convex functions.

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