The Singular CR Yamabe problem and Hausdorff dimension

Huber's theorem for Riemann surfaces states that any complete Riemann surface with finite total curvature is conformal to a compact Riemann surface with finitely many points deleted. We present a CR version of this theorem. We also prove the injectivity of the developing map for spherical CR structures using the positive mass theorem. We shall begin with a review of CR manifolds and some background of the standard CR Yamabe problem beginning with the embeddability of CR manifolds, and the works of Cheng, Malchiodi and Yang on the positive mass theorem and the Sobolev exponent for the Rossi sphere. The work we will talk about is joint work with Paul Yang.