Flexibility of singular Einstein metrics

Mazzeo, Rafe

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

MR Zbl

@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},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {321},
     year = {2008},
     mrnumber = {2521648},
     zbl = {1185.58005},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2008__321__169_0/}
}

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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://archive.numdam.org/item/AST_2008__321__169_0/

Bibliographie
Cité par

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

[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. | DOI | MR | Zbl

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

[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. | DOI | EuDML | Numdam | MR | Zbl

[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. | DOI | MR | Zbl

[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. | EuDML | MR | Zbl

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

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

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

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

[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. | DOI | MR | Zbl

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

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

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

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

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

[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. | DOI | MR | Zbl

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

[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. | DOI | Zbl

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

[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. | DOI | MR | Zbl

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

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

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

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

[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. | DOI | MR | Zbl

[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. | DOI | MR | Zbl