Asymptotic approach to sing ular solutions for the CR Y amabe equation

We study the loss of compactness for optimal functions associated with subcritical approximations of the sharp Folland-Stein-Sobolev embedding in the Heisenberg group. A key ingredient is a fine asymptotic control of the optimal functions by the Jerison--Lee extremals, which attain equality in the critical Sobolev inequality~({\it JAMS}, 1988). When boundary blow-up is ruled out, we show that centered-symmetric maximizers in a Kor\'anyi ball concentrate at its center, and we determine the exact blow-up rate and the pointwise asymptotic profile away from the pole, thereby obtaining a natural counterpart of the classical Atkinson--Brezis--Peletier asymptotics for nearly critical Sobolev problems. We then introduce a class of smooth domains geometrically regular near their characteristic set and extend the analysis to this setting, proving one-point concentration, describing the profile by the Dirichlet Green function, and expressing the exact blow-up rate through a Green-function boundary functional arising from the anisotropic Pohozaev identity.