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

2018/01/23 by Shu-Cheng Chang, Chang, Shu-Cheng, Yingbo Han +2
Mathematics · #32V05 #32V20 #53C56 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1801.07428

openalex publication_date 2018/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the parabolic kernel of the Schrödinger operator
• Differential equations on riemannian manifolds and their geometric applications
• On the CR Poincaré-Lelong equation, Yamabe steady solitons and structures of complete noncompact Sasakian manifolds

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