We will study the CR Yamabe equation for a partially integrable CR structure on the Heisenberg group which is deformed from the standard CR structure. By using the Lyapunov-Schmidt reduction, it is shown that a perturbed standard solution of the CR Yamabe equation is a solution of the deformed CR Yamabe equation, under certain conditions of the deformation. Especially, the deformed CR structure is only partially integrable, in general.
"A Perturbed CR Yamabe Equation on the Heisenberg Group." Tokyo J. Math. 41 (2) 407 - 432, December 2018. https://doi.org/10.3836/tjm/1502179253