CR Yamabe Equation on the Heisenberg Group via the method of moving spheres

In this paper, we classify positive solutions to the CR Yamabe equation on the Heisenberg group ${\mathbb{H}}^n$. We show that all such solutions are Jerison-Lee bubbles, without imposing any finite-energy or a priori symmetry assumptions. This result can be regarded as an analogue for ${\mathbb{H}}^n$ of the celebrated Caffarelli-Gidas-Spruck classification theorem in ${\mathbb{R}}^n$. To establish this, we develop a systematic approach to implement the method of moving spheres in the setting of the Heisenberg group.