The solution of the singular Yamabe problem gives us a tool to study the conformal invariant of a hypersurface. For example, Graham used renormalizing the volume of the singular Yamabe metric to get a conformal invariant energy of a hypersurface which is a generalization of the Willmore energy. For CR manifolds, we also can discuss singular Yamabe problem on CR manifolds. Inspired by Graham, Cheng, Yang, and Zhang used the similar method to get the CR invariant energy E2 of a hypersurface on 3 dim’l strongly pseudoconvex (spc) CR manifold, assuming such solution exists and some behaviors near the hypersurface. In this talk, I will briefly prove the existence of the solution of singular Yamabe equation on (2n+1)-dim’l spc CR manifolds with nonsingular smooth boundary and its behavior near boundary. To prove it, we will use some estimate on subelliptic operator with Hörmander condition and some technique in the proof for Riemannian case by Andersson, Chruciel, and Friedrich. This result also helps us to study the CR invariant of a hypersurface for higher dimension case.

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