L2 curvature and volume renormalization of AHE metrics on 4-manifolds

Mathematical Research Letters

Volumn 8, Issue 1-2, 2001, Pages 171-188

  Anderson, Michael T ^a  

^a STONY BROOK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035532725     PISSN: 10732780     EISSN: None     Source Type: Journal    
DOI: 10.4310/mrl.2001.v8.n2.a6     Document Type: Article

References (16)

1. [1] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry II, Math. Proc. Cambridge Philos. Soc. 78 (1975), 405-432.
2. [2] A. Besse, Einstein Manifolds, Ergeb. Math. Grenzgeb., Springer Verlag, New York, (1987).
3. [3] S. S. Chern, On the curvature integral in a Riemannian manifold, Ann. of Math. 46 (1945), 674-684.
4. [4] S. S. Chern and J. Simons, Characteristic forms and geometric invariants, Ann. of Math. 99 (1974), 48-69.
5. [5] T. Eguchi, P. Gilkey, and A.H. Hanson, Gravitation, Gauge Theories and Differential Geometry, Phys. Rep. 66 (1980), 213-393.
6. [6] C. Fefferman and C. R. Graham, Conformal invariants, Elie Cartan et les Mathematiques d'Aujourd'hui, Astérisque (1985), 95-116.
7. [7] C. R. Graham, Volume and area renormalization for conformally compact Einstein metrics, Rend. Circ. Mat. Palermo (2) Suppl. 63 (2000), 31-42, math.DG/0009042.
8. [8] C. R. Graham and J. M. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991), 186-225.
9. [9] S. W. Hawking and D. N. Page, Thermodynamics of black holes in anti-de Sitter space, Comm. Math. Phys. 87 (1983), 577-588.
10. [10] M. Henningson and K. Skenderis, The holographic Weyl anomaly, J. High Energy Phys. 9807 (1998), 023, hep-th/9806087.
11. [11] N. J. Hitchin, Einstein metrics and the eta-invariant, Boll. Un. Mat. Ital. B (7) 11-B (1997), 95-105.
12. [12] C. LeBrun, H -space with a cosmological constant, Proc. Roy. Soc. London Ser. A380 (1982), 171-185.
13. [13] S. J. Patterson and P. A. Perry, The divisor of Selberg's zeta function for Kleinian groups, Duke Math. J., to appear.
14. [14] R. Penrose and W. Rindler, Spinors and Space-Time, vol. 2, Cambridge Monographs on Mathematical Physics, Cambridge Univ. Press, 1986.
15. [15] I. Rivin and J.-M. Schlenker, On the Schläfli differential formula, preprint, math.DG/0001176.
16. [16] E. Witten, Anti De-Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998), 253-291, hep-th/9802150.