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Opérateurs géométriques, invariants conformes et variétés asymptotiquement hyperboliques
Zindine Djadli, Colin Guillarmou, Marc Herzlich
Panoramas et synthèses 26 (2008), vi+171 pages
Acheter l'ouvrage

Résumé :
En 1985, Fefferman et Graham ont introduit un programme ambitieux (dit de la métrique ambiante) d'étude des invariants locaux de la géométrie conforme. Celui-ci s'est considérablement développé ces dernières années, menant à la définition de nombreux objets nouveaux: opérateurs de Graham-Jenne-Mason-Sparling (GJMS) généralisant ceux de Yamabe et de Paneitz, Q-courbure de Branson... et à des applications parfois spectaculaires et inattendues: classification des variétés conformément plates de dimension 4 à caractéristique d'Euler positive, théorème de pincement conforme^Mde la sphère, etc. Absentes de la stratégie originelle, la géométrie et l'analyse sur les variétés asymptotiquement hyperboliques d'Einstein (ou Poincaré-Einstein) se sont révélées un élément essentiel du programme. L'objectif de ce livre est de présenter un panorama des développements récents et une synthèse des principaux résultats, accessible à des lecteurs ayant une connaissance de base de la géométrie riemannienne.

Abstract:
Geometric operators, conformal invariants and asymptotically hyperbolic manifolds
In 1985, Fefferman and Graham initiated an ambitious program of study of conformal geometry (known as the ambient metricmethod). This has known tremendous developments in the last few years, leading to the definition of a number of new invariants: Graham-Jenne-Mason-Sparling (GJMS) operators generalizing the Yamabe and Paneitz operators, Branson Q-curvatures... and to remarkable applications to conformally flat manifolds of dimension 4 and nonnegative Euler characteristic, or to conformally invariant pinching theorems. An essential role is played in the theory by asymptotically hyperbolic Einstein metrics (or Poincaré-Einstein metrics) associated to a conformal class. The book is devoted to a presentation of the theory together with a description of the latest developments. It should be accessible to all readers having a basic knowledge of Riemannian geometry.


ISBN : 9782-85629-260-0
ISSN : 1272-3835
Publié avec le concours de : Centre National de la Recherche Scientifique

Bibliographie:

1
Adams, David R.
A sharp inequality of J. Moser for higher order derivatives
Ann. of Math. 128 (1988) 385–398
Math Reviews MR960950
2
Albin, Pierre
A renormalized index theorem for some complete asymptotically regular metrics: the Gauss-Bonnet theorem
Adv. Math. 213 (2007) 1–52
Math Reviews MR2331237
3
Albin, Pierre
Renormalizing curvature integrals on Poincaré-Einstein manifolds
Adv. Math. 221 (2009) 140–169
4
Alexakis, Spyros
On the decomposition of global conformal invariants, II
Adv. Math. 206 (2006) 466–502
Math Reviews MR2263712
5
Alexakis, Spyros
On global conformal invariants, I
6
Alexakis, Spyros
The decomposition of global conformal invariants: on a conjecture of Deser and Schwimmer
7
Anderson, Michael T.
L2 curvature and volume renormalization of AHE metrics on 4-manifolds
Math. Res. Lett. 8 (2001) 171–188
Math Reviews MR1825268
8
Anderson, Michael T.
Geometric aspects of the AdS/CFT correspondence
in AdS/CFT correspondence: Einstein metrics and their conformal boundaries
IRMA Lect. Math. Theor. Phys. 8 (2005) 1–31
Math Reviews MR2160865
9
Anderson, Michael T.
Einstein metrics with prescribed conformal infinity on 4-manifolds
Geom. Funct. Anal. 18 (2008) 305–366
Math Reviews MR2421542
10
Anderson, Michael T. and Herzlich, Marc
Unique continuation results for Ricci curvature and applications
J. Geom. Phys. 58 (2008) 179–207
Math Reviews MR2384310
11
Andersson, Lars and Dahl, Mattias
Scalar curvature rigidity for asymptotically locally hyperbolic manifolds
Ann. Global Anal. Geom. 16 (1998) 1–27
Math Reviews MR1616570
12
Aubry, E. and Guillarmou, Colin
Conformal harmonic forms, Branson-Gover operators and Dirichlet problem at infinity
13
Bahri, A. and Coron, J.-M.
The scalar-curvature problem on the standard three-dimensional sphere
J. Funct. Anal. 95 (1991) 106–172
Math Reviews MR1087949
14
Bailey, Toby N. and Eastwood, Michael G. and Gover, A. Rod
Thomas's structure bundle for conformal, projective and related structures
Rocky Mountain J. Math. 24 (1994) 1191–1217
Math Reviews MR1322223
15
Bailey, Toby N. and Eastwood, Michael G. and Graham, C. Robin
Invariant theory for conformal and CR geometry
Ann. of Math. 139 (1994) 491–552
Math Reviews MR1283869
16
Bakry, Dominique and Émery, Michel
Inégalités de Sobolev pour un semi-groupe symétrique
C. R. Acad. Sci. Paris Sér. I Math. 301 (1985) 411–413
Math Reviews MR808640
17
Berline, Nicole and Getzler, Ezra and Vergne, Michèle
Heat kernels and Dirac operators
Springer, 1992
Math Reviews MR1215720
18
Besse, Arthur L.
Einstein manifolds
Springer, 1987
Math Reviews MR867684
19
Biquard, Olivier
Métriques d'Einstein asymptotiquement symétriques
Soc. Math. France, 2000
Math Reviews MR1760319
20
Biquard, Olivier
Métriques autoduales sur la boule
Invent. Math. 148 (2002) 545–607
Math Reviews MR1908060
21
AdS/CFT correspondence: Einstein metrics and their conformal boundaries
European Mathematical Society (EMS), Zürich, 2005
Math Reviews MR2160864
22
Biquard, Olivier
Continuation unique à l'infini pour les métriques d'Einstein
Math. Res. Lett. 15 (2008) 1091–1099
23
Birman, M. Š. and Kren, M. G.
On the theory of wave operators and scattering operators
Dokl. Akad. Nauk SSSR 144 (1962) 475–478
Math Reviews MR0139007
24
Birman, M. Š. and Yafaev, Dmitri
The spectral shift function. The papers of M. G. Kreand their further development
Algebra i Analiz 4 (1992) 1–44
Math Reviews MR1202723
25
Borthwick, David
Spectral theory of infinite-area hyperbolic surfaces
Birkhäuser, 2007
Math Reviews MR2344504
26
Bourguignon, Jean-Pierre
Les variétés de dimension 4 à signature non nulle dont la courbure est harmonique sont d'Einstein
Invent. Math. 63 (1981) 263–286
Math Reviews MR610539
27
Branson, Thomas P.
Differential operators canonically associated to a conformal structure
Math. Scand. 57 (1985) 293–345
Math Reviews MR832360
28
Branson, Thomas P.
Sharp inequalities, the functional determinant, and the complementary series
Trans. Amer. Math. Soc. 347 (1995) 3671–3742
Math Reviews MR1316845
29
Branson, Thomas P. and Chang, Sun-Yung A. and Yang, Paul C.
Estimates and extremals for zeta function determinants on four-manifolds
Comm. Math. Phys. 149 (1992) 241–262
Math Reviews MR1186028
30
Branson, Thomas P. and Gilkey, Peter and Pohjanpelto, Juha
Invariants of locally conformally flat manifolds
Trans. Amer. Math. Soc. 347 (1995) 939–953
Math Reviews MR1282884
31
Branson, Thomas P. and Gover, A. Rod
Conformally invariant operators, differential forms, cohomology and a generalisation of Q-curvature
Comm. Partial Differential Equations 30 (2005) 1611–1669
Math Reviews MR2182307
32
Branson, Thomas P. and rsted, Bent
Explicit functional determinants in four dimensions
Proc. Amer. Math. Soc. 113 (1991) 669–682
Math Reviews MR1050018
33
Bunke, Ulrich and Olbrich, Martin
Selberg zeta and theta functions
Akademie-Verlag, 1995 A differential operator approach
Math Reviews MR1353651
34
Buser, Peter
Geometry and spectra of compact Riemann surfaces
Birkhäuser, 1992
Math Reviews MR1183224
35
Caffarelli, Luis A. and Yang, Yi Song
Vortex condensation in the Chern-Simons Higgs model: an existence theorem
Comm. Math. Phys. 168 (1995) 321–336
Math Reviews MR1324400
36
Čap, Andreas and Gover, A. Rod
Standard tractors and the conformal ambient metric construction
Ann. Global Anal. Geom. 24 (2003) 231–259
Math Reviews MR1996768
37
Čap, Andreas and Schichl, Hermann
Parabolic geometries and canonical Cartan connections
Hokkaido Math. J. 29 (2000) 453–505
Math Reviews MR1795487
38
Carron, Gilles
Déterminant relatif et la fonction Xi
Amer. J. Math. 124 (2002) 307–352
Math Reviews MR1890995
39
Chang, Sun-Yung A. and Fang, H.
A class of variational functionals in conformal geometry
Int. Math. Res. Not. IMRN 7 (2008) 16 pp
40
Chang, Sun-Yung A. and Gursky, Matthew J. and Yang, Paul C.
An equation of Monge-Ampère type in conformal geometry, and four-manifolds of positive Ricci curvature
Ann. of Math. 155 (2002) 709–787
Math Reviews MR1923964
41
Chang, Sun-Yung A. and Gursky, Matthew J. and Yang, Paul C.
A conformally invariant sphere theorem in four dimensions
Publ. Math. Inst. Hautes Études Sci. 98 (2003) 105–143
Math Reviews MR2031200
42
Chang, Sun-Yung A. and Gursky, Matthew J. and Yang, Paul C.
Conformal invariants associated to a measure
Proc. Natl. Acad. Sci. USA 103 (2006) 2535–2540 (electronic)
Math Reviews MR2203156
43
Chang, Sun-Yung A. and Yang, Paul C.
A perturbation result in prescribing scalar curvature on Sn
Duke Math. J. 64 (1991) 27–69
Math Reviews MR1131392
44
Chang, Sun-Yung A. and Yang, Paul C.
Extremal metrics of zeta function determinants on 4-manifolds
Ann. of Math. 142 (1995) 171–212
Math Reviews MR1338677
45
Chang, Sun-Yung Alice and Qing, J. and Yang, Paul C.
Renormalized volumes for conformally compact Einstein manifolds
Sovrem. Mat. Fundam. Napravl. 17 (2006) 129–142
Math Reviews MR2336463
46
Chang, Sun-Yung Alice and Yang, Paul C.
Prescribing Gaussian curvature on S2
Acta Math. 159 (1987) 215–259
Math Reviews MR908146
47
Chen, Chiun-Chuan and Lin, Chang-Shou
Topological degree for a mean field equation on Riemann surfaces
Comm. Pure Appl. Math. 56 (2003) 1667–1727
Math Reviews MR2001443
48
Chruściel, Piotr T. and Delay, Erwann and Lee, John M. and Skinner, Dale N.
Boundary regularity of conformally compact Einstein metrics
J. Differential Geom. 69 (2005) 111–136
Math Reviews MR2169584
49
Cycon, H. L. and Froese, R. G. and Kirsch, W. and Simon, Barry
Schrödinger operators with application to quantum mechanics and global geometry
Springer, 1987
Math Reviews MR883643
50
Demailly, J.-P.
Complex analytic and differential geometry
51
Ding, Weiyue and Jost, Jürgen and Li, Jiayu and Wang, Guofang
Existence results for mean field equations
Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999) 653–666
Math Reviews MR1712560
52
Djadli, Zindine
Existence result for the mean field problem on Riemann surfaces of all genuses
Commun. Contemp. Math. 10 (2008) 205–220
Math Reviews MR2409366
53
Djadli, Zindine and Malchiodi, Andrea
Existence of conformal metrics with constant Q-curvature
Ann. of Math. 168 (2008) 813–858
Math Reviews MR2456884
54
Eastwood, Michael G. and Rice, John W.
Conformally invariant differential operators on Minkowski space and their curved analogues
Comm. Math. Phys. 109 (1987) 207–228
Math Reviews MR880414
55
Falk, C. and Juhl, Andreas
Universal recursive formulas for Q-curvature
56
Fefferman, Charles
Parabolic invariant theory in complex analysis
Adv. in Math. 31 (1979) 131–262
Math Reviews MR526424
57
Fefferman, Charles and Graham, C. Robin
Conformal invariants
in The mathematical heritage of Élie Cartan (Lyon, 1984)
Astérisque hors série (1985) 95–116
Math Reviews MR837196
58
Fefferman, Charles and Graham, C. Robin
Q-curvature and Poincaré metrics
Math. Res. Lett. 9 (2002) 139–151
Math Reviews MR1909634
59
Fefferman, Charles and Graham, C. Robin
The ambient metric
60
Fefferman, Charles and Hirachi, Kengo
Ambient metric construction of Q-curvature in conformal and CR geometries
Math. Res. Lett. 10 (2003) 819–831
Math Reviews MR2025058
61
Fried, David
The zeta functions of Ruelle and Selberg. I
Ann. Sci. École Norm. Sup. 19 (1986) 491–517
Math Reviews MR875085
62
Gauduchon, P.
Connexion canonique en géométrie conforme
(1990)
63
Gover, A. Rod
Aspects of parabolic invariant theory
Rend. Circ. Mat. Palermo (2) Suppl. 59 (1999) 25–47 The 18th Winter School ``Geometry and Physics'' (Srní, 1998)
Math Reviews MR1692257
64
Gover, A. Rod and Leitner, F.
A sub-product construction of Poincare-Einstein metrics
65
Gover, A. Rod and Peterson, Lawrence J.
Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus
Comm. Math. Phys. 235 (2003) 339–378
Math Reviews MR1969732
66
Graham, C. Robin
Volume and area renormalizations for conformally compact Einstein metrics
in The Proceedings of the 19th Winter School ``Geometry and Physics'' (Srn, 1999)
Rend. Circ. Mat. Palermo (2) Suppl. 63 (2000) 31–42
Math Reviews MR1758076
67
Graham, C. Robin
Dirichlet-to-Neumann map for Poincaré-Einstein metrics
Oberwolfach Rep. 2 (2005)
68
Graham, C. Robin
Jet isomorphism for conformal geometry
Arch. Math. (Brno) 43 (2007) 389–415
Math Reviews MR2381784
69
Graham, C. Robin and Hirachi, Kengo
The ambient obstruction tensor and Q-curvature
in AdS/CFT correspondence: Einstein metrics and their conformal boundaries
IRMA Lect. Math. Theor. Phys. 8 (2005) 59–71
Math Reviews MR2160867
70
Graham, C. Robin and Hirachi, Kengo
Inhomogeneous ambient metrics
in Symmetries and overdetermined systems of partial differential equations
IMA Vol. Math. Appl. 144 (2008) 403–420
Math Reviews MR2384722
71
Graham, C. Robin and Jenne, Ralph and Mason, Lionel J. and Sparling, George A. J.
Conformally invariant powers of the Laplacian. I. Existence
J. London Math. Soc. 46 (1992) 557–565
Math Reviews MR1190438
72
Graham, C. Robin and Juhl, Andreas
Holographic formula for Q-curvature
Adv. Math. 216 (2007) 841–853
Math Reviews MR2351380
73
Graham, C. Robin and Lee, John M.
Einstein metrics with prescribed conformal infinity on the ball
Adv. Math. 87 (1991) 186–225
Math Reviews MR1112625
74
Graham, C. Robin and Zworski, Maciej
Scattering matrix in conformal geometry
Invent. Math. 152 (2003) 89–118
Math Reviews MR1965361
75
Guillarmou, Colin
Meromorphic properties of the resolvent on asymptotically hyperbolic manifolds
Duke Math. J. 129 (2005) 1–37
Math Reviews MR2153454
76
Guillarmou, Colin
Generalized Krein formula, determinants and Selberg zeta function in even dimension
77
Guillopé, Laurent and Zworski, Maciej
Polynomial bounds on the number of resonances for some complete spaces of constant negative curvature near infinity
Asymptotic Anal. 11 (1995) 1–22
Math Reviews MR1344252
78
Guillopé, Laurent and Zworski, Maciej
Scattering asymptotics for Riemann surfaces
Ann. of Math. 145 (1997) 597–660
Math Reviews MR1454705
79
Gursky, Matthew J.
Locally conformally flat four- and six-manifolds of positive scalar curvature and positive Euler characteristic
Indiana Univ. Math. J. 43 (1994) 747–774
Math Reviews MR1305946
80
Gursky, Matthew J.
The Weyl functional, de Rham cohomology, and Kähler-Einstein metrics
Ann. of Math. 148 (1998) 315–337
Math Reviews MR1652920
81
Gursky, Matthew J.
The principal eigenvalue of a conformally invariant differential operator, with an application to semilinear elliptic PDE
Comm. Math. Phys. 207 (1999) 131–143
Math Reviews MR1724863
82
Gursky, Matthew J.
Four-manifolds with W+=0 and Einstein constants of the sphere
Math. Ann. 318 (2000) 417–431
Math Reviews MR1800764
83
Gursky, Matthew J. and Viaclovsky, Jeff A.
A fully nonlinear equation on four-manifolds with positive scalar curvature
J. Differential Geom. 63 (2003) 131–154
Math Reviews MR2015262
84
Hejhal, Dennis A.
The Selberg trace formula for PSL(2,<b>R</b>). Vol. 2
Springer, 1983
Math Reviews MR711197
85
Henningson, M. and Skenderis, Kostas
The holographic Weyl anomaly
J. High Energy Phys. 7 (1998) Paper 23, 12 pp.(electronic)
Math Reviews MR1644988
86
Hitchin, Nigel J.
Compact four-dimensional Einstein manifolds
J. Differential Geometry 9 (1974) 435–441
Math Reviews MR0350657
87
Hitchin, Nigel J.
Twistor spaces, Einstein metrics and isomonodromic deformations
J. Differential Geom. 42 (1995) 30–112
Math Reviews MR1350695
88
Hitchin, Nigel J.
Einstein metrics and the eta-invariant
Boll. Un. Mat. Ital. B 11 (1997) 95–105
Math Reviews MR1456253
89
Iwaniec, Henryk
Spectral methods of automorphic forms
Amer. Math. Soc., 2002
Math Reviews MR1942691
90
Joshi, Mark S. and Sá Barreto, Antônio
Inverse scattering on asymptotically hyperbolic manifolds
Acta Math. 184 (2000) 41–86
Math Reviews MR1756569
91
Kato, Tosio
Wave operators and unitary equivalence
Pacific J. Math. 15 (1965) 171–180
Math Reviews MR0180138
92
Kazdan, Jerry L. and Warner, F. W.
Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures
Ann. of Math. 101 (1975) 317–331
Math Reviews MR0375153
93
Kontsevich, Maxim and Vishik, Simeon
Geometry of determinants of elliptic operators
in Functional analysis on the eve of the 21st century, Vol.1 (New Brunswick, NJ, 1993)
Progr. Math. 131 (1995) 173–197
Math Reviews MR1373003
94
Kren, M. G.
On the trace formula in perturbation theory
Mat. Sbornik N.S. 33(75) (1953) 597–626
Math Reviews MR0060742
95
Kren, M. G.
On perturbation determinants and a trace formula for unitary and self-adjoint operators
Dokl. Akad. Nauk SSSR 144 (1962) 268–271
Math Reviews MR0139006
96
Kuiper, N. H.
On conformally-flat spaces in the large
Ann. of Math. 50 (1949) 916–924
Math Reviews MR0031310
97
Kulkarni, Ravindra S.
On the Bianchi Identities
Math. Ann. 199 (1972) 175–204
Math Reviews MR0339004
98
Kulkarni, Ravindra S.
Index theorems of Atiyah-Bott-Patodi and curvature invariants
Les Presses de l'Université de Montréal, Montreal, Que., 1975
Math Reviews MR0440626
99
Labbi, M.-L.
Double forms, curvature structures and the (p,q)-curvatures
Trans. Amer. Math. Soc. 357 (2005) 3971–3992 (electronic)
Math Reviews MR2159696
100
Labbi, M.-L.
Variational properties of the Gauss-Bonnet curvatures
Calc. Var. Partial Differential Equations 32 (2008) 175–189
Math Reviews MR2389988
101
Lax, Peter D. and Phillips, Ralph S.
Scattering theory for automorphic functions
Princeton Univ. Press, 1976 Annals of Mathematics Studies, No. 87
Math Reviews MR0562288
102
LeBrun, Claude R.
H-space with a cosmological constant
Proc. Roy. Soc. London Ser. A 380 (1982) 171–185
Math Reviews MR652038
103
LeBrun, Claude R.
On the topology of self-dual 4-manifolds
Proc. Amer. Math. Soc. 98 (1986) 637–640
Math Reviews MR861766
104
Lee, John M.
The spectrum of an asymptotically hyperbolic Einstein manifold
Comm. Anal. Geom. 3 (1995) 253–271
Math Reviews MR1362652
105
Lee, John M.
Fredholm operators and Einstein metrics on conformally compact manifolds
Mem. Amer. Math. Soc. 183 (2006) 83
Math Reviews MR2252687
106
Lee, John M. and Parker, Thomas H.
The Yamabe problem
Bull. Amer. Math. Soc. (N.S.) 17 (1987) 37–91
Math Reviews MR888880
107
Lesch, Matthias
On the noncommutative residue for pseudodifferential operators with log-polyhomogeneous symbols
Ann. Global Anal. Geom. 17 (1999) 151–187
Math Reviews MR1675408
108
Li, Yan Yan
Prescribing scalar curvature on Sn and related problems. I
J. Differential Equations 120 (1995) 319–410
Math Reviews MR1347349
109
Lin, Chang-Shou
Topological degree for mean field equations on S2
Duke Math. J. 104 (2000) 501–536
Math Reviews MR1781481
110
Lott, John
Optimal transport and Ricci curvature for metric-measure spaces
in Surveys in differential geometry. Vol. XI
Surv. Differ. Geom. 11 (2007) 229–257
Math Reviews MR2408268
111
Malchiodi, Andrea
Compactness of solutions to some geometric fourth-order equations
J. reine angew. Math. 594 (2006) 137–174
Math Reviews MR2248155
112
Maldacena, Juan
The large N limit of superconformal field theories and supergravity
Adv. Theor. Math. Phys. 2 (1998) 231–252
Math Reviews MR1633016
113
Marchioro, Carlo and Pulvirenti, Mario
Mathematical theory of incompressible nonviscous fluids
Springer, 1994
Math Reviews MR1245492
114
Margerin, Christophe
A sharp characterization of the smooth 4-sphere in curvature terms
Comm. Anal. Geom. 6 (1998) 21–65
Math Reviews MR1619838
115
Margerin, Christophe
Géométrie conforme en dimension 4: ce que l'analyse nous apprend
in Séminaire Bourbaki 2004/2005
Astérisque 307 (2006) Exp. No. 950, ix–415–468
Math Reviews MR2296426
116
Mazzeo, Rafe
The Hodge cohomology of a conformally compact metric
J. Differential Geom. 28 (1988) 309–339
Math Reviews MR961517
117
Mazzeo, Rafe
Unique continuation at infinity and embedded eigenvalues for asymptotically hyperbolic manifolds
Amer. J. Math. 113 (1991) 25–45
Math Reviews MR1087800
118
Mazzeo, Rafe R. and Melrose, Richard B.
Meromorphic extension of the resolvent on complete spaces with asymptotically constant negative curvature
J. Funct. Anal. 75 (1987) 260–310
Math Reviews MR916753
119
Melrose, Richard B.
Weyl asymptotics for the phase in obstacle scattering
Comm. Partial Differential Equations 13 (1988) 1431–1439
Math Reviews MR956828
120
Melrose, Richard B.
Geometric scattering theory
Cambridge Univ. Press, 1995
Math Reviews MR1350074
121
Moller, N. M.
Extremals of Dirac operators, spectral determinants and zeta functions, and Branson's conjecture
122
Moser, J.
A sharp form of an inequality by N. Trudinger
Indiana Univ. Math. J. 20 (1970/71) 1077–1092
Math Reviews MR0301504
123
Okikiolu, K.
Critical metrics for the determinant of the Laplacian in odd dimensions
Ann. of Math. 153 (2001) 471–531
Math Reviews MR1829756
124
Onofri, E.
On the positivity of the effective action in a theory of random surfaces
Comm. Math. Phys. 86 (1982) 321–326
Math Reviews MR677001
125
Osgood, B. and Phillips, Ralph S. and Sarnak, P.
Compact isospectral sets of surfaces
J. Funct. Anal. 80 (1988) 212–234
Math Reviews MR960229
126
Osgood, B. and Phillips, Ralph S. and Sarnak, P.
Extremals of determinants of Laplacians
J. Funct. Anal. 80 (1988) 148–211
Math Reviews MR960228
127
Paneitz, S.
A quadratic conformally covariant differential operator for arbitrary pseudo-Riemannian manifolds
(1983)
128
Patterson, S. J.
The limit set of a Fuchsian group
Acta Math. 136 (1976) 241–273
Math Reviews MR0450547
129
Patterson, S. J.
The Selberg zeta-function of a Kleinian group
in Number theory, trace formulas and discrete groups (Oslo, 1987)
(1989) 409–441
Math Reviews MR993330
130
Patterson, S. J. and Perry, Peter A.
The divisor of Selberg's zeta function for Kleinian groups
Duke Math. J. 106 (2001) 321–390 Appendix A by Charles Epstein
Math Reviews MR1813434
131
Paycha, Sylvie and Rosenberg, Steven
Conformal anomalies via canonical traces
in Analysis, geometry and topology of elliptic operators
(2006) 263–294
Math Reviews MR2246772
132
Pedersen, H.
Einstein metrics, spinning top motions and monopoles
Math. Ann. 274 (1986) 35–59
Math Reviews MR834105
133
Perelman, G.
The entropy formula for the Ricci flow and its geometric applications
134
Petkov, V. and Popov, G.
Asymptotic behaviour of the scattering phase for nontrapping obstacles
Ann. Inst. Fourier (Grenoble) 32 (1982) 111–149
Math Reviews MR688023
135
Polyakov, A. M.
Quantum geometry of bosonic strings
Phys. Lett. B 103 (1981) 207–210
Math Reviews MR623209
136
Ratcliffe, John G.
Foundations of hyperbolic manifolds
Springer, 2006
Math Reviews MR2249478
137
Ray, D. B. and Singer, I. M.
R-torsion and the Laplacian on Riemannian manifolds
Advances in Math. 7 (1971) 145–210
Math Reviews MR0295381
138
Reed, Michael and Simon, Barry
Methods of modern mathematical physics. I
Academic Press Inc., 1980 Functional analysis
Math Reviews MR751959
139
Richardson, Ken
Critical points of the determinant of the Laplace operator
J. Funct. Anal. 122 (1994) 52–83
Math Reviews MR1274583
140
Rosenberg, Steven
The Laplacian on a Riemannian manifold
Cambridge Univ. Press, 1997 An introduction to analysis on manifolds
Math Reviews MR1462892
141
Sá Barreto, Antônio
Radiation fields, scattering, and inverse scattering on asymptotically hyperbolic manifolds
Duke Math. J. 129 (2005) 407–480
Math Reviews MR2169870
142
Selberg, Atle
Collected papers. Vol. I
Springer, 1989
Math Reviews MR1117906
143
Sharpe, R. W.
Differential geometry
Springer, 1997
Math Reviews MR1453120
144
Shubin, M. A.
Pseudodifferential operators and spectral theory
Springer, 1987
Math Reviews MR883081
145
Skenderis, Kostas and Solodukhin, Sergey N.
Quantum effective action from the AdS/CFT correspondence
Phys. Lett. B 472 (2000) 316–322
Math Reviews MR1742763
146
Struwe, Michael
The existence of surfaces of constant mean curvature with free boundaries
Acta Math. 160 (1988) 19–64
Math Reviews MR926524
147
Struwe, Michael and Tarantello, Gabriella
On multivortex solutions in Chern-Simons gauge theory
Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. 1 (1998) 109–121
Math Reviews MR1619043
148
Sullivan, Dennis
The density at infinity of a discrete group of hyperbolic motions
Publ. Math. I.H.É.S. 50 (1979) 171–202
Math Reviews MR556586
149
Tang, S. H. and Zworski, Maciej
Potential scattering on the line
150
Tarantello, Gabriella
Multiple condensate solutions for the Chern-Simons-Higgs theory
J. Math. Phys. 37 (1996) 3769–3796
Math Reviews MR1400816
151
Thomas, T. Y.
On conformal geometry
Proc. Natl. Acad. Sci. USA 12 (1926) 352–359
152
Trudinger, Neil S.
On imbeddings into Orlicz spaces and some applications
J. Math. Mech. 17 (1967) 473–483
Math Reviews MR0216286
153
Uhlenbeck, Karen K. and Viaclovsky, Jeff A.
Regularity of weak solutions to critical exponent variational equations
Math. Res. Lett. 7 (2000) 651–656
Math Reviews MR1809291
154
Viaclovsky, Jeff A.
Conformal geometry, contact geometry, and the calculus of variations
Duke Math. J. 101 (2000) 283–316
Math Reviews MR1738176
155
Weyl, Hermann
The classical groups
Princeton Univ. Press, 1997 Their invariants and representations, Fifteenth printing, Princeton Paperbacks
Math Reviews MR1488158
156
Yafaev, Dmitri
Mathematical scattering theory: General Theory
Amer. Math. Soc., 1992
157
Yafaev, Dmitri
Lectures on scattering theory
in Surveys in analysis and operator theory (Canberra, 2001)
Proc. Centre Math. Appl. Austral. Nat. Univ. 40 (2002) 61–88
Math Reviews MR1953480
158
Yang, Yisong
On a system of nonlinear elliptic equations arising in theoretical physics
J. Funct. Anal. 170 (2000) 1–36
Math Reviews MR1736194