CR Sub-Laplacian Comparison and Liouville-Type Theorem in a Complete Noncompact Sasakian Manifold
| Autor: | Jingzhi Tie, Chien Lin, Shu-Cheng Chang, Ting Jung Kuo |
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| Rok vydání: | 2018 |
| Předmět: |
Comparison theorem
Pure mathematics 010102 general mathematics Type (model theory) 01 natural sciences law.invention Sasakian manifold Differential geometry law 0103 physical sciences Torsion (algebra) Mathematics::Differential Geometry 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematics::Symplectic Geometry Laplace operator Manifold (fluid mechanics) Ricci curvature Mathematics |
| Zdroj: | The Journal of Geometric Analysis. 29:1676-1705 |
| ISSN: | 1559-002X 1050-6926 |
| DOI: | 10.1007/s12220-018-0056-9 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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