On the sharp dimension estimate of CR holomorphic functions in Sasakian Manifolds

Abstract

This is the very first 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.

update the first equality in formula (5.12) and some references

References in corpus (4)

• On Yau's uniformization conjecture
• On the three-circle theorem and its applications in Sasakian manifolds
• On the CR Poincaré-Lelong equation, Yamabe steady solitons and structures of complete noncompact Sasakian manifolds
• On Li-Yau gradient estimate for sum of squares of vector fields up to higher step

Cited by in corpus (3)

• Transverse Fully Nonlinear Equations on Sasakian Manifolds and Applications
• On the three-circle theorem and its applications in Sasakian manifolds
• Existence of nonconstant CR-holomorphic functions of polynomial growth in Sasakian Manifolds