On the Sharp Dimension Estimate of CR Holomorphic Functions in Sasakian Manifolds

Abstract

Abstract This is the very 1st paper to 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 Kähler geometry. In this paper, we mainly deal with the problem of the sharp dimension estimate of CR holomorphic functions in a complete noncompact pseudohermitian manifold of vanishing torsion with nonnegative pseudohermitian bisectional curvature.