@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 = {https://www.numdam.org/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 - https://www.numdam.org/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 https://www.numdam.org/item/AST_2008__321__169_0/ %G en %F AST_2008__321__169_0
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. https://www.numdam.org/item/AST_2008__321__169_0/
[1] - "Ricci curvature bounds and Einstein metrics on compact manifolds", J. Amer. Math. Soc. 2 (1989), p. 455-490. | MR | Zbl | DOI
[2] , "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] , "On boundary value problems for Einstein metrics", Geom. Topol. 12 (2008), p. 2009-2045. | MR | Zbl | DOI
[4] - "Convex polyhedra in Lobačevskiĭ spaces", Mat. Sb. (N.S.) 81 (123) (1970), p. 445-478. | MR | Zbl
[5] & - "Hyperideal polyhedra in hyperbolic 3-space", Bull. Soc. Math. France 130 (2002), p. 457-491. | MR | Zbl | EuDML | Numdam | DOI
[6] - Einstein manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 10, Springer, 1987. | MR | Zbl
[7] - "Métriques autoduales sur la boule", Invent. Math. 148 (2002), p. 545-607. | MR | Zbl | DOI
[8] , "Asymptotically symmetric Einstein metrics", SMF/AMS Texts and Monographs, vol. 13, 2006. | MR | Zbl
[9] & - "Parabolic geometries as conformai infinities of Einstein metrics", Arch. Math. (Brno) 42 (2006), p. 85-104. | MR | Zbl | EuDML
[10] & , "A nonlinear Poisson transform for Einstein metrics on product spaces", preprint arXiv:math/0701868. | MR | Zbl | DOI
[11] , & - "Einstein metrics on spheres", Ann. of Math. 162 (2005), p. 557-580. | MR | Zbl | DOI
[12] - "Spectral geometry of singular Riemannian spaces", J. Differential Geom. 18 (1983), p. 575-657. | MR | Zbl | DOI
[13] & - "Curvature and injectivity radius estimates for Einstein -manifolds", J. Amer. Math. Soc. 19 (2006), p. 487-525. | MR | Zbl | DOI
[14] , & - Three-dimensional orbifolds and cone-manifolds, MSJ Memoirs, vol. 5, Mathematical Society of Japan, 2000. | MR | Zbl
[15] - "A generalization of Andreev's theorem", J. Math. Soc. Japan 58 (2006), p. 333-349. | MR | Zbl | DOI
[16] - "Metrics of positive curvature with conic singularities on the sphere", Proc. Amer. Math. Soc. 132 (2004), p. 3349-3355. | MR | Zbl | DOI
[17] & - "Einstein metrics with prescribed conformal infinity on the ball", Adv. Math. 87 (1991), p. 186-225. | MR | Zbl | DOI
[18] , & - "Regenerating singular hyperbolic structures from Sol", J. Differential Geom. 59 (2001), p. 439-478. | MR | Zbl | DOI
[19] & - "Rigidity of hyperbolic cone-manifolds and hyperbolic Dehn surgery", J. Differential Geom. 48 (1998), p. 1-59. | MR | Zbl | DOI
[20] & , "Universal bounds for hyperbolic Dehn surgery", Ann. of Math. 162 (2005), p. 367-421. | MR | Zbl | DOI
[21] - Compact manifolds with special holonomy, Oxford Mathematical Monographs, Oxford University Press, 2000. | MR | Zbl
[22] - "Rigidity and infinitesimal deformability of Einstein metrics", Osaka J. Math. 19 (1982), p. 643-668. | MR | Zbl
[23] & (eds.) - Surveys in differential geometry, vol. VI: Essays on Einstein manifolds, International Press, 2001. | MR | Zbl
[24] - "Fredholm operators and Einstein metrics on conformally compact manifolds", Mem. Amer. Math. Soc. 183 (2006), p. 83. | MR | Zbl
[25] & - "Liouville equation and spherical convex polytopes", Proc. Amer. Math. Soc. 116 (1992), p. 1119-1129. | MR | Zbl | DOI
[26] - "Elliptic theory of differential edge operators. I", Comm. Partial Differential Equations 16 (1991), p. 1615-1664. | MR | Zbl | DOI
[27] & - "Infinitesimal rigidity of hyperbolic cone manifolds and the infinitesimal Stoker problem for hyperbolic polyhedra", in preparation. | Zbl
[28] , & - "Einstein metrics and Ricci solitons with conic singularities", in preparation.
[29] & - "Some remarks on conic degeneration and bending of Poincaré-Einstein metrics", preprint arXiv:0709.1498.
[30] & - "Teichmuller theory of conic surfaces", in preparation. | Zbl | DOI
[31] - "Point singularities and conformai metrics on Riemann surfaces", Proc. Amer. Math. Soc. 103 (1988), p. 222-224. | MR | Zbl | DOI
[32] - "Déformations de métriques Einstein sur des variétés à singularité coniques", Ph.D. Thesis, Thesis, Université Paul Sabatier - Toulouse III, 2005.
[33] - "Hausdorff convergence of Einstein -manifolds", J. Fac. Sci. Univ. Tokyo Sect. IA Math. 35 (1988), p. 411-424. | MR | Zbl
[34] - "Lectures on connected sum constructions in analysis and geometry", preprint http://perso-math.univ-mlv.fr/users/pacard.frank/Lecture-Part-1.pdf.
[35] - Analytic and geometric study of stratified spaces, Lecture Notes in Math., vol. 1768, Springer, 2001. | MR | Zbl
[36] & - "Deforming Euclidean cone -manifolds", Geom. Topol. 11 (2007), p. 1507-1538. | MR | Zbl | DOI
[37] - "A characterization of ideal polyhedra in hyperbolic -space", Ann. of Math. 143 (1996), p. 51-70. | MR | Zbl | DOI
[38] - "Dihedral angles of convex polyhedra", Discrete Comput. Geom. 23 (2000), p. 409-417. | MR | Zbl | DOI
[39] , "Hyperideal circle patterns", Math. Res. Lett. 12 (2005), p. 85-102. | MR | Zbl | DOI
[40] - "Geometrical problems concerning polyhedra in the large", Comm. Pure Appl. Math. 21 (1968), p. 119-168. | MR | Zbl | DOI
[41] - Teichmuller theory in Riemannian geometry, Lectures in Mathematics ETH Zurich, Birkhäuser, 1992. | MR | Zbl
[42] - "Prescribing curvature on compact surfaces with conical singularities", Trans. Amer. Math. Soc. 324 (1991), p. 793-821. | MR | Zbl | DOI
[43] , "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] & - "Metrics of constant curvature 1 with three conical singularities on the 2-sphere", Illinois J. Math. 44 (2000), p. 72-94. | MR | Zbl
[45] - "Local rigidity of 3-dimensional cone-manifolds", J. Differential Geom. 71 (2005), p. 437-506. | MR | Zbl | DOI







