On the rigidity for conformally compact einstein manifolds

International Mathematics Research Notices

Volumn , Issue 21, 2003, Pages 1141-1153

  Qing, Jie ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038329151     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792803209193     Document Type: Article

References (17)

1. M. Anderson, Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds, preprint, 2001, http://arXiv.org/abs/math.DG/0104171.
2. _, Einstein metrics with prescribed conformal infinity on 4-manifolds, preprint, 2001, http://arXiv.org/abs/math.DG/0105243.
3. L. Andersson and M. Dahl, Scalar curvature rigidity for asymptotically locally hyperbolic manifolds. Ann. Global Anal. Geom. 16 (1998), no. 1, 1-27.
4. P. Chruściel and M. Herzlich, The mass of asymptotically hyperbolic Riemannian manifolds, preprint, 2001, http://arXiv.org/abs/math.DG/0110035.
5. J. F. Escobar, The Yamabe problem on manifolds with boundary, J. Differential Geom. 35 (1992), no. 1, 21-84.
6. C. Fefferman and C. R. Graham, Conformal invariants, in Elie Carton et les Mathematiques d'Aujourd'hui, Astérisque (1985), Numero Hors Serie, 95-116.
7. C. R. Graham, Volume and area renormalizations for conformally compact Einstein metrics. The Proceedings of the 19th Winter School "Geometry and Physics" (Srní, 1999), Rend. Circ. Mat. Palermo (2) Suppl. (2000), no. 63, 31-42.
8. C. R. Graham and J. M. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991), no. 2, 186-225.
9. J. M. Lee, The spectrum of an asymptotically hyperbolic Einstein manifold, Comm. Anal. Geom. 3 (1995), no. 1-2, 253-271.
10. J. M. Lee and T. H. Parker, The Yamabe problem, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 1, 37-91.
11. R. Mazzeo, The Hodge cohomology of a conformally compact metric, J. Differential Geom. 28 (1988), no. 2, 309-339.
12. J. G. Ratcliffe, Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics, vol. 149, Springer-Verlag, New York, 1994.
13. R. Schoen, Conformal deformation of a Riemannian metric to constant scalar curvature, J. Differential Geom. 20 (1984), no. 2, 479-495.
14. _, Variational theory for the total scalar curvature functional for Riemannian metrics and related topics, Topics in Calculus of Variations (Montecatini Terme, 1987), Lecture Notes in Math., vol. 1365, Springer, Berlin, 1989, pp. 120-154.
15. X. Wang, Uniqueness of AdS space-time in any dimension, preprint, 2002.
16. E. Witten, A new proof of the positive energy theorem, Comm. Math. Phys. 80 (1981), no. 3, 381-402.
17. X. Zhang, A definition of total energy-momenta and the positive mass theorem for asymptotically hyperbolic 3-manifolds, preprint, 2001.