Flexibility of singular Einstein metrics
Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 169-193

Voir la notice du chapitre de livre provenant de la source Numdam

MR Zbl
Mazzeo, Rafe. Flexibility of singular Einstein metrics, dans Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon, Astérisque, no. 321 (2008), pp. 169-193. http://geodesic.mathdoc.fr/item/AST_2008__321__169_0/
@incollection{AST_2008__321__169_0,
     author = {Mazzeo, Rafe},
     title = {Flexibility of singular {Einstein} metrics},
     booktitle = {G\'eom\'etrie diff\'erentielle, physique math\'ematique, math\'ematiques et soci\'et\'e (I) : Volume en l'honneur de Jean Pierre Bourguignon},
     editor = {Hijazi Oussama},
     series = {Ast\'erisque},
     pages = {169--193},
     year = {2008},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {321},
     mrnumber = {2521648},
     zbl = {1185.58005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AST_2008__321__169_0/}
}
TY  - CHAP
AU  - Mazzeo, Rafe
TI  - Flexibility of singular Einstein metrics
BT  - Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
AU  - Collectif
ED  - Hijazi Oussama
T3  - Astérisque
PY  - 2008
SP  - 169
EP  - 193
IS  - 321
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/AST_2008__321__169_0/
LA  - en
ID  - AST_2008__321__169_0
ER  - 
%0 Book Section
%A Mazzeo, Rafe
%T Flexibility of singular Einstein metrics
%B Géométrie différentielle, physique mathématique, mathématiques et société (I) : Volume en l'honneur de Jean Pierre Bourguignon
%A Collectif
%E Hijazi Oussama
%S Astérisque
%D 2008
%P 169-193
%N 321
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/AST_2008__321__169_0/
%G en
%F AST_2008__321__169_0

[1] M. T. Anderson - "Ricci curvature bounds and Einstein metrics on compact manifolds", J. Amer. Math. Soc. 2 (1989), p. 455-490. | MR | Zbl | DOI

[2] M. T. Anderson, "Topics in conformally compact Einstein metrics", in Perspectives in Riemannian geometry, CRM Proc. Lecture Notes, vol. 40, Amer. Math. Soc., 2006, p. 1-26. | MR | Zbl | DOI

[3] M. T. Anderson, "On boundary value problems for Einstein metrics", Geom. Topol. 12 (2008), p. 2009-2045. | MR | Zbl | DOI

[4] E. M. Andreev - "Convex polyhedra in Lobačevskiĭ spaces", Mat. Sb. (N.S.) 81 (123) (1970), p. 445-478. | MR | Zbl

[5] X. Bao & F. Bonahon - "Hyperideal polyhedra in hyperbolic 3-space", Bull. Soc. Math. France 130 (2002), p. 457-491. | MR | Zbl | EuDML | Numdam | DOI

[6] A. L. Besse - Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 10, Springer, 1987. | MR | Zbl

[7] O. Biquard - "Métriques autoduales sur la boule", Invent. Math. 148 (2002), p. 545-607. | MR | Zbl | DOI

[8] O. Biquard, "Asymptotically symmetric Einstein metrics", SMF/AMS Texts and Monographs, vol. 13, 2006. | MR | Zbl

[9] O. Biquard & R. Mazzeo - "Parabolic geometries as conformai infinities of Einstein metrics", Arch. Math. (Brno) 42 (2006), p. 85-104. | MR | Zbl | EuDML

[10] O. Biquard & R. Mazzeo, "A nonlinear Poisson transform for Einstein metrics on product spaces", preprint arXiv:math/0701868. | MR | Zbl | DOI

[11] C. P. Boyer, K. Galicki & J. Kollár - "Einstein metrics on spheres", Ann. of Math. 162 (2005), p. 557-580. | MR | Zbl | DOI

[12] J. Cheeger - "Spectral geometry of singular Riemannian spaces", J. Differential Geom. 18 (1983), p. 575-657. | MR | Zbl | DOI

[13] J. Cheeger & G. Tian - "Curvature and injectivity radius estimates for Einstein 4-manifolds", J. Amer. Math. Soc. 19 (2006), p. 487-525. | MR | Zbl | DOI

[14] D. Cooper, C. D. Hodgson & S. P. Kerckhoff - Three-dimensional orbifolds and cone-manifolds, MSJ Memoirs, vol. 5, Mathematical Society of Japan, 2000. | MR | Zbl

[15] R. Díaz - "A generalization of Andreev's theorem", J. Math. Soc. Japan 58 (2006), p. 333-349. | MR | Zbl | DOI

[16] A. Eremenko - "Metrics of positive curvature with conic singularities on the sphere", Proc. Amer. Math. Soc. 132 (2004), p. 3349-3355. | MR | Zbl | DOI

[17] C. R. Graham & J. M. Lee - "Einstein metrics with prescribed conformal infinity on the ball", Adv. Math. 87 (1991), p. 186-225. | MR | Zbl | DOI

[18] M. Heusener, J. Porti & E. Suárez - "Regenerating singular hyperbolic structures from Sol", J. Differential Geom. 59 (2001), p. 439-478. | MR | Zbl | DOI

[19] C. D. Hodgson & S. P. Kerckhoff - "Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery", J. Differential Geom. 48 (1998), p. 1-59. | MR | Zbl | DOI

[20] C. D. Hodgson & S. P. Kerckhoff, "Universal bounds for hyperbolic Dehn surgery", Ann. of Math. 162 (2005), p. 367-421. | MR | Zbl | DOI

[21] D. D. Joyce - Compact manifolds with special holonomy, Oxford Mathematical Monographs, Oxford University Press, 2000. | MR | Zbl

[22] N. Koiso - "Rigidity and infinitesimal deformability of Einstein metrics", Osaka J. Math. 19 (1982), p. 643-668. | MR | Zbl

[23] C. Lebrun & M. Wang (eds.) - Surveys in differential geometry, vol. VI: Essays on Einstein manifolds, International Press, 2001. | MR | Zbl

[24] J. M. Lee - "Fredholm operators and Einstein metrics on conformally compact manifolds", Mem. Amer. Math. Soc. 183 (2006), p. 83. | MR | Zbl

[25] F. Luo & G. Tian - "Liouville equation and spherical convex polytopes", Proc. Amer. Math. Soc. 116 (1992), p. 1119-1129. | MR | Zbl | DOI

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

[27] R. Mazzeo & G. Montcouquiol - "Infinitesimal rigidity of hyperbolic cone manifolds and the infinitesimal Stoker problem for hyperbolic polyhedra", in preparation. | Zbl

[28] R. Mazzeo, F. Pacard & H. Weiss - "Einstein metrics and Ricci solitons with conic singularities", in preparation.

[29] R. Mazzeo & M. Singer - "Some remarks on conic degeneration and bending of Poincaré-Einstein metrics", preprint arXiv:0709.1498.

[30] R. Mazzeo & H. Weiss - "Teichmuller theory of conic surfaces", in preparation. | Zbl | DOI

[31] R. C. Mcowen - "Point singularities and conformai metrics on Riemann surfaces", Proc. Amer. Math. Soc. 103 (1988), p. 222-224. | MR | Zbl | DOI

[32] G. Montcouquiol - "Déformations de métriques Einstein sur des variétés à singularité coniques", Ph.D. Thesis, Thesis, Université Paul Sabatier - Toulouse III, 2005.

[33] H. Nakajima - "Hausdorff convergence of Einstein 4-manifolds", J. Fac. Sci. Univ. Tokyo Sect. IA Math. 35 (1988), p. 411-424. | MR | Zbl

[34] F. Pacard - "Lectures on connected sum constructions in analysis and geometry", preprint http://perso-math.univ-mlv.fr/users/pacard.frank/Lecture-Part-1.pdf.

[35] M. J. Pflaum - Analytic and geometric study of stratified spaces, Lecture Notes in Math., vol. 1768, Springer, 2001. | MR | Zbl

[36] J. Porti & H. Weiss - "Deforming Euclidean cone 3-manifolds", Geom. Topol. 11 (2007), p. 1507-1538. | MR | Zbl | DOI

[37] I. Rivin - "A characterization of ideal polyhedra in hyperbolic 3-space", Ann. of Math. 143 (1996), p. 51-70. | MR | Zbl | DOI

[38] J.-M. Schlenker - "Dihedral angles of convex polyhedra", Discrete Comput. Geom. 23 (2000), p. 409-417. | MR | Zbl | DOI

[39] J.-M. Schlenker, "Hyperideal circle patterns", Math. Res. Lett. 12 (2005), p. 85-102. | MR | Zbl | DOI

[40] J. J. Stoker - "Geometrical problems concerning polyhedra in the large", Comm. Pure Appl. Math. 21 (1968), p. 119-168. | MR | Zbl | DOI

[41] A. J. Tromba - Teichmuller theory in Riemannian geometry, Lectures in Mathematics ETH Zurich, Birkhäuser, 1992. | MR | Zbl

[42] M. Troyanov - "Prescribing curvature on compact surfaces with conical singularities", Trans. Amer. Math. Soc. 324 (1991), p. 793-821. | MR | Zbl | DOI

[43] M. Troyanov, "On the moduli space of singular Euclidean surfaces", in Handbook of Teichmuller theory. Vol. I, IRMA Lect. Math. Theor. Phys., vol. 11, Eur. Math. Soc., Zürich, 2007, p. 507-540. | MR | Zbl

[44] M. Umehara & K. Yamada - "Metrics of constant curvature 1 with three conical singularities on the 2-sphere", Illinois J. Math. 44 (2000), p. 72-94. | MR | Zbl

[45] H. Weiss - "Local rigidity of 3-dimensional cone-manifolds", J. Differential Geom. 71 (2005), p. 437-506. | MR | Zbl | DOI