Classification of positive entire solutions of the CR Yamabe equation on the Heisenberg group

We prove that, for every $n\ge 2$, every positive entire solution of the critical CR Yamabe equation $4Δ_b u = n^2 u^{(Q+2)/(Q-2)}$, $Q=2n+2$, on the Heisenberg group $\mathbb H^n$ is a Jerison-Lee bubble. No integrability, decay, boundedness, or symmetry is assumed. Together with the theorem of Cat