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Eigenvalue estimate of the Dirac operator and Rigidity of Poincare-Einstein metrics
Chen, Daguang1; Wang, Fang2; Zhang, Xiao3,4
2019-10-01
Source PublicationMATHEMATISCHE ZEITSCHRIFT
ISSN0025-5874
Volume293Issue:1-2Pages:485-502
AbstractWe 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.
KeywordEigenvalue Dirac operator Boundary condition Yamabe invariant Poincare-Einstein metric
DOI10.1007/s00209-018-2210-2
Language英语
Funding ProjectNSF 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 Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000486234100019
PublisherSPRINGER HEIDELBERG
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/35721
Collection数学所
Corresponding AuthorZhang, Xiao
Affiliation1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
2.Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
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.
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