Scattering matrix in conformal geometry
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Exposé no. 22, 14 p.
Graham, C. Robin 1 ; Zworski, Maciej 2

1 Department of Mathematics, University of Washington, Box 354350,Seattle, WA 98195
2 Department of Mathematics, University of California Berkeley, CA 94720
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     mrnumber = {1860694},
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Graham, C. Robin; Zworski, Maciej. Scattering matrix in conformal geometry. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2000-2001), Exposé no. 22, 14 p. http://archive.numdam.org/item/SEDP_2000-2001____A22_0/

[1] M. Anderson, L 2 curvature and volume renormalization for AHE metrics on 4-manifolds, Math. Res. Lett. 8 (2001), to appear, math-DG/0011051. | MR | Zbl

[2] T. Branson, Sharp inequalities, the functional determinant, and the complementary series, Trans. AMS 347 (1995), 3671-3742. | MR | Zbl

[3] S.-Y.A. Chang, J. Qing, and P.C. Yang, Compactification of a class of conformally flat 4-manifolds, Invent. Math. 147(2000), 65-93. | MR | Zbl

[4] C. Fefferman and C.R. Graham, Conformal invariants, in The mathematical heritage of Élie Cartan (Lyon, 1984). Astérisque, 1985, Numero Hors Serie, 95–116. | Numdam | MR | Zbl

[5] C.R. Graham, Volume and area renormalizations for conformally compact Einstein metrics, Rend. Circ. Mat. Palermo, Ser.II, Suppl. 63 (2000), 31-42. | MR | Zbl

[6] C.R. Graham, R. Jenne, L.J. Mason, and G.A.J. Sparling Conformally invariant powers of the Laplacian. I. Existence. J. London Math. Soc. (2) 46 (1992), 557–565. | MR | Zbl

[7] C.R. Graham and J. Lee, Einstein metrics with prescribed conformal infinity on the ball, Adv. Math. 87 (1991), 186-225. | MR | Zbl

[8] C.R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999), 52-64, hep-th/9901021. | MR | Zbl

[9] C.R. Graham and M. Zworski, Scattering matrix in conformal geometry, in preparation.

[10] L. Guillopé and M. Zworski, Scattering asymptotics for Riemann surfaces, Ann. Math. 145(1997), 597-660. | MR | Zbl

[11] M. Henningson and K. Skenderis, The holographic Weyl anomaly, J. High Ener. Phys. 07 (1998), 023, hep-th/9806087; Holography and the Weyl anomaly, hep-th/9812032. | MR | Zbl

[12] M. Joshi and A. Sá Barreto, Inverse scattering on asymptotically hyperbolic manifolds, Acta Math. 184(2000), 41–86. | MR | Zbl

[13] M. Joshi and A. Sá Barreto, The wave group on asymptotically hyperbolic manifolds, to appear in J. Funct. Anal. | MR | Zbl

[14] J. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2(1998), 231–252, hep-th/9711200. | MR | Zbl

[15] R. Mazzeo, The Hodge cohomology of a conformally compact metric, J. Differential Geom. 28(1988), 309–339. | MR | Zbl

[16] R. Mazzeo, Elliptic theory of differential edge operators. I, Comm. Partial Differential Equations 16(1991), 1615–1664. | MR | Zbl

[17] R. Mazzeo and R. Melrose, Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature, J. Funct. Anal. 75 (1987), 260-310. | MR | Zbl

[18] R.B. Melrose, Geometric Scattering Theory. Cambridge University Press, 1995. | MR | Zbl

[19] R. Melrose and M. Zworski, Scattering metrics and geodesic flow at infinity. Invent. Math. 124(1996), 389-436. | MR | Zbl

[20] R. Newton, Scattering theory of waves and particles, McGraw-Hill Book Co., New York-Toronto-London 1966. | MR

[21] S. J. Patterson and P. A. Perry, The divisor of Selberg’s zeta function for Kleinian groups, Duke Math. J. 106 (2001), 321-390. Appendix A by C. Epstein, An asymptotic volume formula for convex cocompact hyperbolic manifolds. | Zbl

[22] P. Perry, The Laplace operator on a hyperbolic manifold. II. Eisenstein series and the scattering matrix, J. reine. angew. Math. 398 (1989), 67-91. | MR | Zbl

[23] E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998), 253-290, hep-th/9802150. | MR | Zbl

[24] M. Zworski, Resonances in physics and geometry. Notices Amer. Math. Soc. 46 (1999), 319–328. | MR | Zbl