Controlled Fölner sequences and ergodic mappings
Romain Tessera

Amenable connected Lie groups and their lattices have "controlled" Fölner sequences. This means that they are, quantitatively speaking, as amenable as any non compact locally compact group can be. Among various consequences, we will see that these groups admit isometric actions on Lp spaces whose orbits are "almost" quasi-isometrically embedded.