The Cheeger constant of simply connected, solvable Lie groups
  We show that the Cheeger isoperimetric constant of a solvable simply connected Lie group $G$ with Lie algebra $\G$ is $h(G)=\max_{H\in\G,||H||=1} \tr(\ad (H))$. 
Norbert Peyerimhoff, Evangelia Samiou