Geodesic
Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces
Tim Austin1 ; Assaf Naor2 orcid ; Romain Tessera3
1New York University, USA
2New York University, United States
3Université Paris-Sud, Orsay, France
Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 497-522

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DOI

Let H denote the discrete Heisenberg group, equipped with a word metric dW​ associated to some finite symmetric generating set. We show that if (X,∥⋅∥) is a p-convex Banach space then for any Lipschitz function f:H→X there exist x,y∈H with dW​(x,y) arbitrarily large and
DOI : 10.4171/ggd/193
Classification : 46-XX, 20-XX, 30-XX
Mots-clés : Bi-Lipschitz embedding, Heisenberg group, superreflexive Banach spaces

Tim Austin  1   ; Assaf Naor  2   ; Romain Tessera  3

1 New York University, USA
2 New York University, United States
3 Université Paris-Sud, Orsay, France 
Tim Austin; Assaf Naor; Romain Tessera. Sharp quantitative nonembeddability of the Heisenberg group into superreflexive Banach spaces. Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 497-522. doi: 10.4171/ggd/193
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     title = {Sharp quantitative nonembeddability of the {Heisenberg} group into superreflexive {Banach} spaces},
     journal = {Groups, geometry, and dynamics},
     pages = {497--522},
     year = {2013},
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     number = {3},
     doi = {10.4171/ggd/193},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/193/}
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