Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires
Séminaire de théorie spectrale et géométrie, Tome 22 (2003-2004), pp. 153-182.
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     author = {Lupo-Krebs, Guillaume and Pajot, Herv\'e},
     title = {Dimensions conformes, espaces {Gromov-hyperboliques} et ensembles autosimilaires},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {153--182},
     publisher = {Institut Fourier},
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     volume = {22},
     year = {2003-2004},
     zbl = {1069.30038},
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     language = {fr},
     url = {http://www.numdam.org/item/TSG_2003-2004__22__153_0/}
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Lupo-Krebs, Guillaume; Pajot, Hervé. Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires. Séminaire de théorie spectrale et géométrie, Tome 22 (2003-2004), pp. 153-182. http://www.numdam.org/item/TSG_2003-2004__22__153_0/

[1] C.J. Bishop, J. Tyson, Conformal dimension of the antenna set, Proceedings of the American Mathematical Society Volume 129 ( 2001), 3631-3636. | MR 1860497 | Zbl 0972.30010

[2] M. Bonk, J. Hei Nonen, P. Koskeia, Uniformizing Gromov hyperbolic spaces, Asterisque 270 ( 2001). | MR 1829896 | Zbl 0970.30010

[3] M. Bonk, B. Kleiner, Rigidity of quasi-möbius group actions, Journal of Differential Geometry Volume 61 ( 2002), 81-106. | MR 1949785 | Zbl 1044.37015

[4] M. Bonk, B. Kleiner, Quasisymmetric parametrizations of two dimensionnal metric spheres, Inventionnes Mathematicae Volume 150 ( 2002), 127-183. | MR 1930885 | Zbl 1037.53023

[5] M. Bonk, B. Kleiner, Conformal dimension and Gromovhyperbolic groups with 2-sphere boundary, Preprint. | Zbl 1087.20033

[6] M. Bourdon, Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geometric And Functional Analysis Volume 7 ( 1997), 245-268. | MR 1445387 | Zbl 0876.53020

[7] M. Bourdon, H. Pajot, Poincare inequalities and quasiconformal structure on the boundary of some hyperbolic buildings, Proceedings of the American Mathematical Society Volume 127 ( 1999), 2315-2324. | MR 1610912 | Zbl 0924.30030

[8] M. Bourdon, H. Pajot, Rigidity of quasi isometries for some hyperbolic buildings, Commentarii Mathematici Helvetici Volume 75 ( 2000), 701-736. | MR 1789183 | Zbl 0976.30011

[9] M. Bourdon, H. Pajot, Quasi-conformal geometry and hyperbolic geometry, in "Rigidity in Dynamics and Geometry", edité par M. Burger and A. Iozzi, Springer ( 2002), 1-15. | MR 1919393 | Zbl 1002.30012

[10] M. Bourdon, H. Pajot, Cohomologie lp et espaces de Besov, Journal für die Reine und Angewandte Mathematik Volume 558 ( 2003), 85-108. | MR 1979183 | Zbl 1044.20026

[11] D. Burago, Y. BuragoS. Ivanov, A course in metric geometry,Graduate Studies in Mathematics 33 ( 2001), American Mathematical Society. | MR 1835418 | Zbl 0981.51016

[12] J. Cheeger, Differentiability of Lipschitz functions on metric spaces, Geometric and Functional Analysis Volume 9 ( 1999), 428-517. | MR 1708448 | Zbl 0942.58018

[13] M. Coornaert, T. Delzant, A. Papadopou Los, Géométrie et théorie des groupes, Les groupes hyperboliques de Gromov, Lecture Notes in Mathematics Volume 1441 ( 1990), Springer-Verlag. | MR 1075994 | Zbl 0727.20018

[14] G. David, S. Semmes, Fractured fractals and broken dreams, Oxford Lecture Series in Mathematics and its Applications Volume 7, Oxford University Press ( 1997). | MR 1616732 | Zbl 0887.54001

[15] E. Ghys, P. De La Harpe, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics Volume 83 ( 1990), Birkhauser. | MR 1086648 | Zbl 0731.20025

[16] J. Heinonen, A capacity estimate on Carnot groups, Bulletin des Sciences Mathématiques Volume119 ( 1995), 475-484. | MR 1354248 | Zbl 0842.22007

[17] J. Heinonen, Lectures on analysis on metric spaces, Universitext, Springer ( 2001). | MR 1800917 | Zbl 0985.46008

[18] J. Heinonen, P. Koskela, Definitions of quasiconformality, Inventiones Mathematicae Volume 120 ( 1995), 61-79. | MR 1323982 | Zbl 0832.30013

[19] J. Heinonen, P. Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Matematica Volume 181 ( 1998),1-61. | MR 1654771 | Zbl 0915.30018

[20] J. Heinonen, P. Koskela, N. Shanmugalingam, J. Tyson, Sobolev classes of Banach space-valued functions and quasiconformal mappings, Journal d'Analyse Mathématique Volume 85 ( 2001), 87-139. | MR 1869604 | Zbl 1013.46023

[21] D. Jerison, The Poincare inequality for vector flelds satisfying Hörmander condition, Duke Mathematical Journal Volume 53 ( 1986), 503-523. | MR 850547 | Zbl 0614.35066

[22] M. Kapovich, B. Kleiner, Hyperbolic groups with low-dimensional boundary, Annales Scientifiques de l'Ecole Normale Supérieure Volume 33 ( 2000), 647-669. | Numdam | MR 1834498 | Zbl 0989.20031

[23] S. Keith, T. Laakso, Conformal Assouad dimension and modulus, Preprint ( 2003). | MR 2135168 | Zbl 1108.28008

[24] A. Korányi, H. M. Reimann, Foundations for the theory of quasiconformal mappings on the Heisenberg group, Advances in Mathematics Volume 111 ( 1995), 1-87. | MR 1317384 | Zbl 0876.30019

[25] T. Laakso, Ahlfors Q-regular spaces with arbitrary Q > 1 admitting weak Poincare inequality, Geometric and Functional Analysis Volume 10 ( 2000), 111-123. | MR 1748917 | Zbl 0962.30006

[26] C. Loewner, On the conformal capacity in space, Journal o f Mathematical Mechanic Volume 8 ( 1959), 411-414. | MR 104785 | Zbl 0086.28203

[27] P. Mattila, Geometry of sets and measures in Euclidean spaces, Cambridge University Press ( 1995). | MR 1333890 | Zbl 0819.28004

[28] J. Mitchell, On Carnot-Caratheodory metrics, Journal of Differential Geometry Volume 21 ( 1985), 35-45. | MR 806700 | Zbl 0554.53023

[29] G.D. Mostow, Strong rigidity of locally symmetric spaces, Annals of Mathematical Studies Volume 78, Princeton University Press ( 1973). | MR 385004 | Zbl 0265.53039

[30] H. Pajot, Analyse dans les espaces singuliers ; Rectiflabilité ; Géométrie quasi-conforme et géométrie hyperbolique, Texte pour l'habilitation à diriger des recherches, Université de Cergy-Pontoise ( 2002).

[31] P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang 1, Annals of Mathematics Volume 129 ( 1989), 1-60. | MR 979599 | Zbl 0678.53042

[32] N. Shanmugalingam, Newtonian spaces : an extension of Sobolev spaces to metric measure spaces, Revista Mathematica Iberoamericana Volume 16 ( 2000), 243-279. | MR 1809341 | Zbl 0974.46038

[33] D. Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, dans "Riemann surfaces and related topics :Proceedings of the 1978 Stony Brook conference" PrincetonUniversity Press ( 1981), 465-496. | MR 624833 | Zbl 0567.58015

[34] J. Tyson, Quasiconformality and quasisymmetry in metric spaces, Annales Academiae Scientiarum Fennicae Volume 23 ( 1998), 525-548. | MR 1642158 | Zbl 0910.30022

[35] J. Vaisälä, Lectures on n-dimensional quasiconformal mappings, Lectures Notes in Mathematics Volume 229 ( 1971). | MR 454009

[36] N. Varopoulos, Fonctions harmoniques sur les groupes de Lie, Comptes Rendus de l'Académie des Sciences de Paris Volume 309 ( 1987), 519-521. | MR 892879 | Zbl 0614.22002