Eigenvalue estimate of the Dirac operator and Rigidity of Poincare-Einstein metrics

doi:10.1007/s00209-018-2210-2

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	Eigenvalue estimate of the Dirac operator and Rigidity of Poincare-Einstein metrics
	Chen, Daguang 1; Wang, Fang 2; Zhang, Xiao3,4
	2019-10-01
发表期刊	MATHEMATISCHE ZEITSCHRIFT
ISSN	0025-5874
卷号	293 期号:1-2 页码:485-502
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.
关键词	Eigenvalue Dirac operator Boundary condition Yamabe invariant Poincare-Einstein metric
DOI	10.1007/s00209-018-2210-2
语种	英语
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
WOS类目	Mathematics
WOS记录号	WOS:000486234100019
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35721
专题	数学所
通讯作者	Zhang, Xiao
作者单位	1.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
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.