@article{TSG_2006-2007__25__159_0, author = {Pierre Pansu}, title = {Plongements quasiisom\'etriques du groupe de {Heisenberg} dans $L^p$, d{\textquoteright}apr\`es {Cheeger,} {Kleiner,} {Lee,} {Naor}}, journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie}, pages = {159--176}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {25}, year = {2006-2007}, doi = {10.5802/tsg.253}, mrnumber = {2478814}, zbl = {1170.46304}, language = {fr}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.253/} }
TY - JOUR AU - Pierre Pansu TI - Plongements quasiisométriques du groupe de Heisenberg dans $L^p$, d’après Cheeger, Kleiner, Lee, Naor JO - Séminaire de théorie spectrale et géométrie PY - 2006-2007 SP - 159 EP - 176 VL - 25 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.253/ DO - 10.5802/tsg.253 LA - fr ID - TSG_2006-2007__25__159_0 ER -
%0 Journal Article %A Pierre Pansu %T Plongements quasiisométriques du groupe de Heisenberg dans $L^p$, d’après Cheeger, Kleiner, Lee, Naor %J Séminaire de théorie spectrale et géométrie %D 2006-2007 %P 159-176 %V 25 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.253/ %R 10.5802/tsg.253 %G fr %F TSG_2006-2007__25__159_0
Pierre Pansu. Plongements quasiisométriques du groupe de Heisenberg dans $L^p$, d’après Cheeger, Kleiner, Lee, Naor. Séminaire de théorie spectrale et géométrie, Volume 25 (2006-2007), pp. 159-176. doi : 10.5802/tsg.253. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.253/
[1] Luigi Ambrosio Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces, Adv. Math., Volume 159 (2001) no. 1, pp. 51-67 | MR | Zbl
[2] Sanjeev Arora; Elad Hazan; Satyen Kale; IEEE Computer Society approximation to SPARSEST CUT in time, 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2004) (2004)
[3] Sanjeev Arora; James R. Lee; Assaf Naor Euclidean distortion and the sparsest cut, J. Amer. Math. Soc., Volume 21 (2008) no. 1, p. 1-21 (electronic) | MR | Zbl
[4] Patrice Assouad Espaces métriques, plongements, facteurs, U.E.R. Mathématique, Université Paris XI, Orsay, 1977 (Thèse de doctorat, Publications Mathématiques d’Orsay, No. 223-7769) | MR | Zbl
[5] Patrice Assouad Plongements lipschitziens dans , Bull. Soc. Math. France, Volume 111 (1983) no. 4, pp. 429-448 | Numdam | MR | Zbl
[6] J. Bourgain On Lipschitz embedding of finite metric spaces in Hilbert space, Israel J. Math., Volume 52 (1985) no. 1-2, pp. 46-52 | MR | Zbl
[7] J. Bourgain The metrical interpretation of superreflexivity in Banach spaces, Israel J. Math., Volume 56 (1986) no. 2, pp. 222-230 | MR | Zbl
[8] Jean Bretagnolle; Didier Dacunha-Castelle; Jean-Louis Krivine Lois stables et espaces , Ann. Inst. H. Poincaré Sect. B (N.S.), Volume 2 (1965/1966), pp. 231-259 | Numdam | MR | Zbl
[9] Jeff Cheeger; Bruce Kleiner Differentiating maps into , and the geometry of BV functions, arXiv :math/0611954
[10] Jeff Cheeger; Bruce Kleiner On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces, Inspired by S. S. Chern (Nankai Tracts Math.), Volume 11, World Sci. Publ., Hackensack, NJ, 2006, pp. 129-152 | MR
[11] Ennio De Giorgi Nuovi teoremi relativi alle misure -dimensionali in uno spazio ad dimensioni, Ricerche Mat., Volume 4 (1955), pp. 95-113 | MR | Zbl
[12] Michel Marie Deza; Monique Laurent Geometry of cuts and metrics, Algorithms and Combinatorics, 15, Springer-Verlag, Berlin, 1997 | MR | Zbl
[13] Per Enflo On the nonexistence of uniform homeomorphisms between -spaces, Ark. Mat., Volume 8 (1969), p. 103-105 (1969) | MR | Zbl
[14] Bruno Franchi; Raul Serapioni; Francesco Serra Cassano On the structure of finite perimeter sets in step 2 Carnot groups, J. Geom. Anal., Volume 13 (2003) no. 3, pp. 421-466 | MR | Zbl
[15] Michel X. Goemans Semidefinite programming in combinatorial optimization, Math. Programming, Volume 79 (1997) no. 1-3, Ser. B, pp. 143-161 Lectures on mathematical programming (ismp97) (Lausanne, 1997) | MR | Zbl
[16] M. Gromov Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) (London Math. Soc. Lecture Note Ser.), Volume 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1-295 | MR
[17] M. Gromov Random walk in random groups, Geom. Funct. Anal., Volume 13 (2003) no. 1, pp. 73-146 | MR | Zbl
[18] Juha Heinonen; Pekka Koskela From local to global in quasiconformal structures, Proc. Nat. Acad. Sci. U.S.A., Volume 93 (1996) no. 2, pp. 554-556 | MR | Zbl
[19] M. Ĭ. Kadecʼ On the connection between weak and strong convergence, Dopovidi Akad. Nauk Ukraïn. RSR, Volume 1959 (1959), pp. 949-952 | MR | Zbl
[20] Shizuo Kakutani Mean ergodic theorem in abstract -spaces, Proc. Imp. Acad., Tokyo, Volume 15 (1939), pp. 121-123 | MR | Zbl
[21] Subhash Khot; Nisheeth K. Vishnoi; IEEE Computer Society The Unique Games Conjecture, Integrality Gap for Cut Problems and the Embeddability of Negative Type Metrics into ., 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005) (2005), pp. 53-62
[22] V. Klee Mappings into normed linear spaces, Fund. Math., Volume 49 (1960/1961), pp. 25-34 | MR | Zbl
[23] James Lee; Assaf Naor; IEEE Computer Society metrics on the Heisenberg group and the Goemans-Linial conjecture, 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2006) (2005), p. 99-108, Preprint (2006)
[24] Nathan Linial; J. Matousek Squared metrics into , Open Problems (2002)
[25] Nathan Linial; Eran London; Yuri Rabinovich The geometry of graphs and some of its algorithmic applications, Combinatorica, Volume 15 (1995) no. 2, pp. 215-245 | MR | Zbl
[26] Scott D. Pauls The large scale geometry of nilpotent Lie groups, Comm. Anal. Geom., Volume 9 (2001) no. 5, pp. 951-982 | MR | Zbl
[27] Stephen Semmes On the nonexistence of bi-Lipschitz parameterizations and geometric problems about -weights, Rev. Mat. Iberoamericana, Volume 12 (1996) no. 2, pp. 337-410 | MR | Zbl
[28] Romain Tessera Asymptotic isoperimetry on groups and uniform embeddings into Banach spaces Preprint (2006)
[29] Guoliang Yu The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space, Invent. Math., Volume 139 (2000) no. 1, pp. 201-240 | MR | Zbl
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