Majorations asymptotiques du barycentre convexe d'une mesure de probabilité sur les espaces homogènes S2×R, H2×R et l'espace de Heisenberg H3

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 S2×R, H2×R or the Heisenberg space H3. The upper bounds are obtained with the construction of almost affine convex functions.