Eigenvalue estimate of the Dirac operator and Rigidity of Poincare-Einstein metrics
文献类型：期刊论文
| 作者 | Chen, Daguang2; Wang, Fang3; Zhang, Xiao1,4
|
| 刊名 | MATHEMATISCHE ZEITSCHRIFT
 |
| 出版日期 | 2019-10-01 |
| 卷号 | 293期号:1-2页码:485-502 |
| 关键词 | Eigenvalue Dirac operator Boundary condition Yamabe invariant Poincare-Einstein metric |
| ISSN号 | 0025-5874 |
| DOI | 10.1007/s00209-018-2210-2 |
| 英文摘要 | We re-visit the eigenvalue estimate of the Dirac operator on spin manifolds with boundary in terms of the first eigenvalues of conformal Laplace operator as well as the conformal mean curvature operator. These problems were studied earlier by Hijazi-Montiel-Zhang and Raulot and we re-prove them under weaker assumption that a boundary chirality operator exists. Moreover, on these spin manifolds with boundary, we show that any C3,alpha conformal compactification of some Poincare-Einstein metric must be the standard hemisphere when the first nonzero eigenvalue of the Dirac operator achieves its lowest value, and any C3,alpha conformal compactification of some Poincare-Einstein metric must be the flat ball in Euclidean space when the first positive eigenvalue of the boundary Dirac operator achieves certain value relating to the second Yamabe invariant. In two cases the Poincare-Einstein metrics are standard hyperbolic metric. |
| 资助项目 | NSF of China[11571345] ; NSF of China[11731001] ; NSF of China[11471180] ; NSF of China[11831005] ; NSF of China[11571233] ; NSF of China[11871331] ; HLM ; NCMIS ; CEMS ; HCMS of Chinese Academy of Sciences |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000486234100019 |
| 出版者 | SPRINGER HEIDELBERG |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/35720]  |
| 专题 | 数学所 |
| 通讯作者 | Zhang, Xiao |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China 3.Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Chen, Daguang,Wang, Fang,Zhang, Xiao. Eigenvalue estimate of the Dirac operator and Rigidity of Poincare-Einstein metrics[J]. MATHEMATISCHE ZEITSCHRIFT,2019,293(1-2):485-502. |
| APA | Chen, Daguang,Wang, Fang,&Zhang, Xiao.(2019).Eigenvalue estimate of the Dirac operator and Rigidity of Poincare-Einstein metrics.MATHEMATISCHE ZEITSCHRIFT,293(1-2),485-502. |
| MLA | Chen, Daguang,et al."Eigenvalue estimate of the Dirac operator and Rigidity of Poincare-Einstein metrics".MATHEMATISCHE ZEITSCHRIFT 293.1-2(2019):485-502. |
入库方式： OAI收割
来源：数学与系统科学研究院
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