Liouville-type results for the CR Yamabe equation in the Heisenberg group

Abstract

We obtain Liouville-type results for solutions to the CR Yamabe equation in ${\mathbb{H}}^n$, which extend a result obtained by Jerison and Lee for solutions in $L^{2+2/n}({\mathbb{H}}^n)$. We obtain our results under either pointwise conditions or integral conditions at infinity. In particular, our results hold for all bounded solutions when $n=2$ and solutions satisfying a pointwise decay assumption when $n\ge 3$. The proofs rely on integral estimates combined with a suitable divergence formula.

Theorem 1.1 is improved and Theorem 1.4 is added