Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires

Guillaume Lupo-Krebs; Hervé Pajot

Séminaire de théorie spectrale et géométrie (2003-2004)

  • Volume: 22, page 153-182
  • ISSN: 1624-5458

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Lupo-Krebs, Guillaume, and Pajot, Hervé. "Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires." Séminaire de théorie spectrale et géométrie 22 (2003-2004): 153-182. <http://eudml.org/doc/114482>.

@article{Lupo2003-2004,
author = {Lupo-Krebs, Guillaume, Pajot, Hervé},
journal = {Séminaire de théorie spectrale et géométrie},
keywords = {conformal dimension; Fuchsian building; weak tangent space; moduli of curves; Sierpinski carpet; hyperbolic group},
language = {fre},
pages = {153-182},
publisher = {Institut Fourier},
title = {Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires},
url = {http://eudml.org/doc/114482},
volume = {22},
year = {2003-2004},
}

TY - JOUR
AU - Lupo-Krebs, Guillaume
AU - Pajot, Hervé
TI - Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires
JO - Séminaire de théorie spectrale et géométrie
PY - 2003-2004
PB - Institut Fourier
VL - 22
SP - 153
EP - 182
LA - fre
KW - conformal dimension; Fuchsian building; weak tangent space; moduli of curves; Sierpinski carpet; hyperbolic group
UR - http://eudml.org/doc/114482
ER -

References

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  1. [1] C.J. BISHOP, J. TYSON, Conformal dimension of the antenna set, Proceedings of the American Mathematical Society Volume 129 ( 2001), 3631-3636. Zbl0972.30010MR1860497
  2. [2] M. BONK, J. HEI NONEN, P. KOSKEIA, Uniformizing Gromov hyperbolic spaces, Asterisque 270 ( 2001). Zbl0970.30010MR1829896
  3. [3] M. BONK, B. KLEINER, Rigidity of quasi-möbius group actions, Journal of Differential Geometry Volume 61 ( 2002), 81-106. Zbl1044.37015MR1949785
  4. [4] M. BONK, B. KLEINER, Quasisymmetric parametrizations of two dimensionnal metric spheres, Inventionnes Mathematicae Volume 150 ( 2002), 127-183. Zbl1037.53023MR1930885
  5. [5] M. BONK, B. KLEINER, Conformal dimension and Gromovhyperbolic groups with 2-sphere boundary, Preprint. Zbl1087.20033
  6. [6] M. BOURDON, Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geometric And Functional Analysis Volume 7 ( 1997), 245-268. Zbl0876.53020MR1445387
  7. [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. Zbl0924.30030MR1610912
  8. [8] M. BOURDON, H. PAJOT, Rigidity of quasi isometries for some hyperbolic buildings, Commentarii Mathematici Helvetici Volume 75 ( 2000), 701-736. Zbl0976.30011MR1789183
  9. [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. Zbl1002.30012MR1919393
  10. [10] M. BOURDON, H. PAJOT, Cohomologie lp et espaces de Besov, Journal für die Reine und Angewandte Mathematik Volume 558 ( 2003), 85-108. Zbl1044.20026MR1979183
  11. [11] D. BURAGO, Y. BURAGO S. IVANOV, A course in metric geometry,Graduate Studies in Mathematics 33 ( 2001), American Mathematical Society. Zbl0981.51016MR1835418
  12. [12] J. CHEEGER, Differentiability of Lipschitz functions on metric spaces, Geometric and Functional Analysis Volume 9 ( 1999), 428-517. Zbl0942.58018MR1708448
  13. [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. Zbl0727.20018MR1075994
  14. [14] G. DAVID, S. SEMMES, Fractured fractals and broken dreams, Oxford Lecture Series in Mathematics and its Applications Volume 7, Oxford University Press ( 1997). Zbl0887.54001MR1616732
  15. [15] E. GHYS, P. DE LA HARPE, Sur les groupes hyperboliques d'après Mikhael Gromov, Progress in Mathematics Volume 83 ( 1990), Birkhauser. Zbl0731.20025MR1086648
  16. [16] J. HEINONEN, A capacity estimate on Carnot groups, Bulletin des Sciences Mathématiques Volume119 ( 1995), 475-484. Zbl0842.22007MR1354248
  17. [17] J. HEINONEN, Lectures on analysis on metric spaces, Universitext, Springer ( 2001). Zbl0985.46008MR1800917
  18. [18] J. HEINONEN, P. KOSKELA, Definitions of quasiconformality, Inventiones Mathematicae Volume 120 ( 1995), 61-79. Zbl0832.30013MR1323982
  19. [19] J. HEINONEN, P. KOSKELA, Quasiconformal maps in metric spaces with controlled geometry, Acta Matematica Volume 181 ( 1998),1-61. Zbl0915.30018MR1654771
  20. [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. Zbl1013.46023MR1869604
  21. [21] D. JERISON, The Poincare inequality for vector flelds satisfying Hörmander condition, Duke Mathematical Journal Volume 53 ( 1986), 503-523. Zbl0614.35066MR850547
  22. [22] M. KAPOVICH, B. KLEINER, Hyperbolic groups with low-dimensional boundary, Annales Scientifiques de l'Ecole Normale Supérieure Volume 33 ( 2000), 647-669. Zbl0989.20031MR1834498
  23. [23] S. KEITH, T. LAAKSO, Conformal Assouad dimension and modulus, Preprint ( 2003). Zbl1108.28008MR2135168
  24. [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. Zbl0876.30019MR1317384
  25. [25] T. LAAKSO, Ahlfors Q-regular spaces with arbitrary Q &gt; 1 admitting weak Poincare inequality, Geometric and Functional Analysis Volume 10 ( 2000), 111-123. Zbl0962.30006MR1748917
  26. [26] C. LOEWNER, On the conformal capacity in space, Journal o f Mathematical Mechanic Volume 8 ( 1959), 411-414. Zbl0086.28203MR104785
  27. [27] P. MATTILA, Geometry of sets and measures in Euclidean spaces, Cambridge University Press ( 1995). Zbl0819.28004MR1333890
  28. [28] J. MITCHELL, On Carnot-Caratheodory metrics, Journal of Differential Geometry Volume 21 ( 1985), 35-45. Zbl0554.53023MR806700
  29. [29] G.D. MOSTOW, Strong rigidity of locally symmetric spaces, Annals of Mathematical Studies Volume 78, Princeton University Press ( 1973). Zbl0265.53039MR385004
  30. [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. [31] P. PANSU, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang 1, Annals of Mathematics Volume 129 ( 1989), 1-60. Zbl0678.53042MR979599
  32. [32] N. SHANMUGALINGAM, Newtonian spaces : an extension of Sobolev spaces to metric measure spaces, Revista Mathematica Iberoamericana Volume 16 ( 2000), 243-279. Zbl0974.46038MR1809341
  33. [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. Zbl0567.58015MR624833
  34. [34] J. TYSON, Quasiconformality and quasisymmetry in metric spaces, Annales Academiae Scientiarum Fennicae Volume 23 ( 1998), 525-548. Zbl0910.30022MR1642158
  35. [35] J. VAISÄLÄ, Lectures on n-dimensional quasiconformal mappings, Lectures Notes in Mathematics Volume 229 ( 1971). Zbl0221.30031MR454009
  36. [36] N. VAROPOULOS, Fonctions harmoniques sur les groupes de Lie, Comptes Rendus de l'Académie des Sciences de Paris Volume 309 ( 1987), 519-521. Zbl0614.22002MR892879

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