CR Sub-Laplacian Comparison and Liouville-Type Theorem in a Complete Noncompact Sasakian Manifold

Shu Cheng Chang, Ting Jung Kuo, Chien Lin, Jingzhi Tie

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4 Citations (Scopus)


In this paper, we first obtain the sub-Laplacian comparison theorem in a complete noncompact pseudohermitian manifold of vanishing torsion (i.e., Sasakian manifold). Second, we derive the subgradient estimate for positive pseudoharmonic functions in a complete noncompact pseudohermitian manifold which satisfies the CR sub-Laplacian comparison property. It functions as the CR analog of Yau’s gradient estimate. As a consequence, we have the natural CR analog of Liouville-type theorems in a complete noncompact Sasakian manifold of nonnegative pseudohermitian Ricci curvature tensors.

Original languageEnglish
Pages (from-to)1676-1705
Number of pages30
JournalJournal of Geometric Analysis
Issue number2
Publication statusPublished - 2019 Apr 15



  • CR Bochner formula
  • Liouville-type theorem
  • Pseudohermitian Ricci
  • Pseudohermitian torsion
  • Ricatti inequality
  • Sasakain manifold
  • Sub-Laplacian comparison theorem
  • Subgradient estimate

ASJC Scopus subject areas

  • Geometry and Topology

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