Quasi-isometric rigidity conjecture for completely solvable Lie groups

Let $S$ and $S'$ be completely solvable Lie groups.

Quasi-isometric rigidity conjecture. $S$ and $S'$ are quasi-isometric if and only if they are isomorphic.

This conjecture predicts that the quasi-isometry class completely determines a completely solvable Lie group up to isomorphism. The paper identifies quasi-isometry classification results for Carnot-Sol type and metabelian groups as special cases, while the general statement remains open.