Géométrie quasiconforme, analyse au bord des espaces métriques hyperboliques et rigidités [d'après Mostow, Pansu, Bourdon, Pajot, Bonk, Kleiner...]

Haïssinsky, Peter

Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 993, 42 p.

MR Zbl | 2 citations dans Numdam

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     title = {G\'eom\'etrie quasiconforme, analyse au bord des espaces m\'etriques hyperboliques et rigidit\'es [d'apr\`es {Mostow,} {Pansu,} {Bourdon,} {Pajot,} {Bonk,} {Kleiner...]}},
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     note = {talk:993},
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     year = {2009},
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Haïssinsky, Peter. Géométrie quasiconforme, analyse au bord des espaces métriques hyperboliques et rigidités [d'après Mostow, Pansu, Bourdon, Pajot, Bonk, Kleiner...], dans Séminaire Bourbaki Volume 2007/2008 Exposés 982-996, Astérisque, no. 326 (2009), Exposé no. 993, 42 p.. https://www.numdam.org/item/AST_2009__326__321_0/

Bibliographie
Cité par

[1] J. M. Alonso et al. - Notes on word hyperbolic groups, in Group theory from a geometrical viewpoint (Trieste, 1990), World Sci. Publ., River Edge, NJ, 1991, Edited by H. Short, p. 3-63. | MR | Zbl

[2] Z. M. Balogh, P. Koskela & S. Rogovin - Absolute continuity of quasiconformal mappings on curves, Geom. Funct. Anal. 17 (2007), p. 645-664. | MR | Zbl | DOI

[3] M. Bonk - Quasiconformal geometry of fractals, in International Congress of Mathematicians. Vol. II, Eur. Math. Soc, Zürich, 2006, p. 1349-1373. | MR | Zbl

[4] M. Bonk & B. Kleiner - Quasisymmetric parametrizations of two-dimensional metric spheres, Invent Math. 150 (2002), p. 127-183. | MR | Zbl | DOI

[5] M. Bonk & B. Kleiner -, Rigidity for quasi-Möbius group actions, J. Differential Geom. 61 (2002), p. 81-106. | MR | Zbl | DOI

[6] M. Bonk & B. Kleiner -, Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary, Geom. Topol. 9 (2005), p. 219-246. | MR | Zbl | EuDML | DOI

[7] M. Bonk & B. Kleiner -, Quasi-hyperbolic planes in hyperbolic groups, Proc. Amer. Math. Soc. 133 (2005), p. 2491-2494. | MR | Zbl | DOI

[8] M. Bonk & O. Schramm - Embeddings of Gromov hyperbolic spaces, Geom. Funct. Anal. 10 (2000), p. 266-306. | MR | Zbl | DOI

[9] M. Bourdon - Structure conforme au bord et flot géodésique d'un CAT(-1)-espace, Enseign. Math. 41 (1995), p. 63-102. | MR | Zbl

[10] M. Bourdon -, Sur le birapport au bord des CAT (-1)-espaces, Publ. Math. I.H.É.S. 83 (1996), p. 95-104. | MR | Zbl | EuDML | Numdam | DOI

[11] M. Bourdon -, Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geom. Funct. Anal. 7 (1997), p. 245-268. | MR | Zbl | DOI

[12] M. Bourdon -, Sur les immeubles fuchsiens et leur type de quasi-isométrie, Ergodic Theory Dynam. Systems 20 (2000), p. 343-364. | MR | Zbl | DOI

[13] M. Bourdon & H. Pajot - Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings, Proc. Amer. Math. Soc. 127 (1999), p. 2315-2324. | MR | Zbl | DOI

[14] M. Bourdon & H. Pajot -, Rigidity of quasi-isometries for some hyperbolic buildings, Comment. Math. Helv. 75 (2000), p. 701-736. | MR | Zbl | DOI

[15] M. Bourdon & H. Pajot -, Quasi-conformal geometry and hyperbolic geometry, in Rigidity in dynamics and geometry (Cambridge, 2000), Springer, 2002, p. 1-17. | MR | Zbl

[16] M. Bourdon & H. Pajot -, Cohomologie $ℓ_{p}$ et espaces de Besov, J. reine angew. Math. 558 (2003), p. 85-108. | MR | Zbl

[17] B. H. Bowditch - A topological characterisation of hyperbolic groups, J. Amer. Math. Soc. 11 (1998), p. 643-667. | MR | Zbl | DOI

[18] B. H. Bowditch -, Convergence groups and configuration spaces, in Geometric group theory down under (Canberra, 1996), de Gruyter, 1999, p. 23-54. | MR | Zbl

[19] J. W. Cannon - The theory of negatively curved spaces and groups, in Ergodic theory, symbolic dynamics, and hyperbolic spaces (Trieste, 1989), Oxford Sci. Publ., Oxford Univ. Press, 1991, p. 315-369. | MR | Zbl

[20] J. W. Cannon -, The combinatorial Riemann mapping theorem, Acta Math. 173 (1994), p. 155-234. | MR | Zbl | DOI

[21] J. W. Cannon, W. J. Floyd & W. R. Parry - Sufficiently rich families of planar rings, Ann. Acad. Sci. Fenn. Math. 24 (1999), p. 265-304. | MR | Zbl | EuDML

[22] J. W. Cannon & E. L. Swenson - Recognizing constant curvature discrete groups in dimension 3, Trans. Amer. Math. Soc. 350 (1998), p. 809-849. | MR | Zbl | DOI

[23] A. Casson & D. Jungreis - Convergence groups and Seifert fibered 3-manifolds, Invent. Math. 118 (1994), p. 441-456. | MR | Zbl | EuDML | DOI

[24] J. Cheeger - Differentiability of Lipschitz functions on metric measure spaces, Geom. Fund. Anal. 9 (1999), p. 428-517. | MR | Zbl | DOI

[25] R. Chow - Groups quasi-isometric to complex hyperbolic space, Trans. Amer. Math. Soc. 348 (1996), p. 1757-1769. | MR | Zbl | DOI

[26] C. Connell - Minimal Lyapunov exponents, quasiconformal structures, and rigidity of non-positively curved manifolds, Ergodic Theory Dynam. Systems 23 (2003), p. 429-446. | MR | Zbl | DOI

[27] M. Coornaert - Mesures de Patterson-Sullivan sur le bord d'un espace hyperbolique au sens de Gromov, Pacific J. Math. 159 (1993), p. 241-270. | MR | Zbl | DOI

[28] M. Coornaert, T. Delzant & A. Papadopoulos - Géométrie et théorie des groupes, Lecture Notes in Math., vol. 1441, Springer, 1990. | MR | Zbl

[29] A. Douady & J. H. Hubbard - A proof of Thurston's topological characterization of rational functions, Acta Math. 171 (1993), p. 263-297. | MR | Zbl | DOI

[30] P. Eberlein & B. O'Neill - Visibility manifolds, Pacific J. Math. 46 (1973), p. 45-109. | MR | Zbl | DOI

[31] D. Gabai - Convergence groups are Fuchsian groups, Bull. Amer. Math. Soc. (N.S.) 25 (1991), p. 395-402. | MR | Zbl | DOI

[32] É. Ghys & P. De La Harpe (éds.) - Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Math., vol. 83, Birkhäuser, 1990. | Zbl | MR

[33] M. Gromov - Groups of polynomial growth and expanding maps, Publ. Math. I.H.É.S. 53 (1981), p. 53-73. | MR | Zbl | Numdam | DOI

[34] M. Gromov -, Hyperbolic groups, in Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, 1987, p. 75-263. | MR | Zbl | DOI

[35] M. Gromov & P. Pansu -Rigidity of lattices : an introduction, in Geometric topology : recent developments (Montecatini Terme, 1990), Lecture Notes in Math., vol. 1504, Springer, 1991, p. 39-137. | MR | Zbl

[36] M. Gromov & W. Thurston - Pinching constants for hyperbolic manifolds, Invent. Math. 89 (1987), p. 1-12. | MR | Zbl | EuDML | DOI

[37] P. Haïssinsky - Empilements de cercles et modules combinatoires, à paraître aux Ann. Inst. Fourier. | MR | Zbl | EuDML | Numdam

[38] P. Haïssinsky & K. M. Pilgrim - Thurston obstructions and Ahlfors regular conformal dimension, J. Math. Pures Appl. 90 (2008), p. 229-241. | MR | Zbl | DOI

[39] P. Haïssinsky & K. M. Pilgrim -, Coarse expanding conformal dynamics, à paraître dans Astérisque. | MR | Zbl | Numdam

[40] U. Hamenstädt - A geometric characterization of negatively curved locally symmetric spaces, J. Differential Geom. 34 (1991), p. 193-221. | MR | Zbl | DOI

[41] J. Heinonen - A capacity estimate on Carnot groups, Bull. Sci. Math. 119 (1995), p. 475-484. | MR | Zbl

[42] J. Heinonen -, Lectures on analysis on metric spaces, Universitext, Springer, 2001. | MR | Zbl | DOI

[43] J. Heinonen & P. Koskela - Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), p. 1-61. | MR | Zbl | DOI

[44] J. Heinonen, P. Koskela, N. Shanmugalingam & J. T. Tyson - Sobolev classes of Banach space-valued functions and quasiconformal mappings, J. Anal. Math. 85 (2001), p. 87-139. | MR | Zbl | DOI

[45] I. Kapovich & N. Benakli - Boundaries of hyperbolic groups, in Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), Contemp. Math., vol. 296, Amer. Math. Soc, 2002, p. 39-93. | MR | Zbl | DOI

[46] S. Keith & T. Laakso - Conformal Assouad dimension and modulus, Geom. Funct. Anal. 14 (2004), p. 1278-1321. | MR | Zbl | DOI

[47] B. Kleiner - The asymptotic geometry of negatively curved spaces : uniformization, geometrization and rigidity, in International Congress of Mathematicians. Vol. II, Eur. Math. Soc, Zürich, 2006, p. 743-768. | MR | Zbl

[48] P. Koebe - Kontaktprobleme der konformen abbildung, Ber. Sächs. Akad. Wiss. Leipzig 88 (1936), p. 141-164. | Zbl

[49] J. Lelong-Ferrand - Transformations conformes et quasi-conformes des variétés riemanniennes compactes (démonstration de la conjecture de A. Lichnerowicz), Acad. Roy. Belg. Cl. Sci. Mém. Coll. in-8° 39 (1971), p. 44. | MR | Zbl

[50] J. Lelong-Ferrand -, Invariants conformes globaux sur les variétés riemanniennes, J. Differential Geometry 8 (1973), p. 487-510. | MR | Zbl | DOI

[51] C. Loewner - On the conformal capacity in space, J. Math. Mech. 8 (1959), p. 411-414. | MR | Zbl

[52] G. A. Margulis - The isometry of closed manifolds of constant negative curvature with the same fundamental group, Dokl. Akad. Nauk SSSR 192 (1970), p. 736-737. | MR | Zbl

[53] G. A. Margulis & G. D. Mostow - The differential of a quasi-conformal mapping of a Carnot-Carathéodory space, Geom. Funct. Anal. 5 (1995), p. 402-433. | MR | Zbl | EuDML | DOI

[54] J. Mitchell - On Carnot-Carathéodory metrics, J. Differential Geom. 21 (1985), p. 35-45. | MR | Zbl | DOI

[55] G. D. Mostow - Quasi-conformal mappings in $n$ -space and the rigidity of hyperbolic space forms, Publ. Math. I.H.É.S. 34 (1968), p. 53-104. | MR | Zbl | EuDML | Numdam | DOI

[56] G. D. Mostow -, Strong rigidity of locally symmetric spaces, Princeton Univ. Press, 1973, Annals of Mathematics Studies, No. 78. | MR | Zbl

[57] P. Pansu - Dimension conforme et sphère à l'infini des variétés à courbure négative, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), p. 177-212. | MR | Zbl | DOI

[58] P. Pansu -, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. 129 (1989), p. 1-60. | MR | Zbl | DOI

[59] F. Paulin - Un groupe hyperbolique est déterminé par son bord, J. London Math. Soc. 54 (1996), p. 50-74. | MR | Zbl | DOI

[60] H. M. Reimann - An estimate for pseudoconformal capacities on the sphere, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), p. 315-324. | MR | Zbl | DOI

[61] D. Sullivan - The density at infinity of a discrete group of hyperbolic motions, Publ. Math. I.H.É.S. 50 (1979), p. 171-202. | MR | Zbl | EuDML | Numdam | DOI

[62] D. Sullivan -, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, in Riemann surfaces and related topics : Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978), Ann. of Math. Stud., vol. 97, Princeton Univ. Press, 1981, p. 465-496. | MR | Zbl

[63] D. Sullivan -, Discrete conformal groups and measurable dynamics, Bull. Amer. Math. Soc. (N.S.) 6 (1982), p. 57-73. | MR | Zbl | DOI

[64] D. Sullivan -, Seminar on hyperbolic geometry and conformal dynamical systems, prépublication I.H.É.S., 1982.

[65] P. Tukia - On quasiconformal groups, J. Analyse Math. 46 (1986), p. 318-346. | MR | Zbl | DOI

[66] P. Tukia -, Homeomorphic conjugates of Fuchsian groups, J. reine angew. Math. 391 (1988), p. 1-54. | MR | Zbl | EuDML

[67] P. Tukia -, Convergence groups and Gromov's metric hyperbolic spaces, New Zealand J. Math. 23 (1994), p. 157-187. | MR | Zbl

[68] P. Tukia & J. Väisälä - Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), p. 97-114. | MR | Zbl | DOI

[69] J. T. Tyson - Quasiconformality and quasisymmetry in metric measure spaces, Ann. Acad. Sci. Fenn. Math. 23 (1998), p. 525-548. | MR | Zbl | EuDML

[70] J. T. Tyson -, Metric and geometric quasiconformality in Ahlfors regular Loewner spaces, Conform. Geom. Dyn. 5 (2001), p. 21-73. | MR | Zbl | DOI

[71] J. Väisälä - Lectures on $n$ -dimensional quasiconformal mappings, Lecture Notes in Math., vol. 229, Springer, 1971. | MR | Zbl

[72] J. Väisälä -, Quasi-Möbius maps, J. Analyse Math. 44 (1984/85), p. 218-234. | MR | DOI

[73] X. Xie - Quasi-isometric rigidity of Fuchsian buildings, Topology 45 (2006), p. 101-169. | MR | Zbl | DOI