In this talk, we will focus on the CR analogue of Yau's uniformization conjecture in a complete noncompact pseudohermitian (2n+1)-manifold of vanishing torsion (i.e. Sasakian manifold) which is an odd dimensional counterpart of Kahler geometry. And we obtain the sharp dimension estimate of CR holomorphic functions in a complete noncompact pseudohermitian manifold of vanishing torsion with nonnegative pseudohermitian bisectional curvature. This is a joint work with Professor Shu-Cheng Chang and Dr Chien Lin.
