Comptes Rendus
Analyse mathématique, Topologie
Some comments on Laakso graphs and sets of differences
Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 515-521.

We recall a variation of a construction due to Laakso [3], also used by Lang and Plaut [3] of a doubling metric space X that cannot be embedded into any Hilbert space. We give a more concrete version of this construction and motivated by the results of Olson & Robinson [6], we consider the Kuratowski embedding Φ(X) of X into L (X) and prove that Φ(X)-Φ(X) is not doubling.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.70

Alexandros Margaris 1 ; James C. Robinson 1

1 Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2020__358_4_515_0,
     author = {Alexandros Margaris and James C. Robinson},
     title = {Some comments on {Laakso} graphs and sets of differences},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {515--521},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {4},
     year = {2020},
     doi = {10.5802/crmath.70},
     language = {en},
}
TY  - JOUR
AU  - Alexandros Margaris
AU  - James C. Robinson
TI  - Some comments on Laakso graphs and sets of differences
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 515
EP  - 521
VL  - 358
IS  - 4
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.70
LA  - en
ID  - CRMATH_2020__358_4_515_0
ER  - 
%0 Journal Article
%A Alexandros Margaris
%A James C. Robinson
%T Some comments on Laakso graphs and sets of differences
%J Comptes Rendus. Mathématique
%D 2020
%P 515-521
%V 358
%N 4
%I Académie des sciences, Paris
%R 10.5802/crmath.70
%G en
%F CRMATH_2020__358_4_515_0
Alexandros Margaris; James C. Robinson. Some comments on Laakso graphs and sets of differences. Comptes Rendus. Mathématique, Volume 358 (2020) no. 4, pp. 515-521. doi : 10.5802/crmath.70. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.70/

[1] Patrice Assouad Plongements Lipschitziens dans n , Bull. Soc. Math. Fr., Volume 111 (1983), pp. 429-448 | DOI | MR | Zbl

[2] Juha Heinonen Geometric Embeddings of Metric Spaces, Report. University of Jyväskylä. Department of Mathematics and Statistics, 90, University of Jyväskylä, 2003 | MR | Zbl

[3] Tomi J. Laakso Plane with A -weighted metric not bilipschitz embeddable to n , Bull. Lond. Math. Soc., Volume 34 (2002) no. 6, pp. 667-676 | DOI | MR | Zbl

[4] Urs Lang; Conrad Plaut Bilipschitz embeddings of metric spaces into space forms, Geom. Dedicata, Volume 87 (2001) no. 1-3, pp. 285-307 | DOI | MR | Zbl

[5] Alexandros Margaris Dimensions, Embeddings and Iterated Function Systems, Ph. D. Thesis, University of Warwick (UK) (2019)

[6] Eric J. Olson; James C. Robinson Almost bi-Lipschitz embeddings and almost homogeneous sets, Trans. Am. Math. Soc., Volume 362 (2010) no. 1, pp. 145-168 | DOI | MR | Zbl

[7] James C. Robinson Dimensions, Embeddings and Attractors, Cambridge Tracts in Mathematics, 186, Cambridge University Press, 2011 | MR | Zbl

[8] James C. Robinson Log-Lipschitz embeddings of homogeneous sets with sharp logarithmic exponents and slicing products of balls, Proc. Am. Math. Soc., Volume 142 (2014) no. 4, pp. 1275-1288 | DOI | MR | Zbl

[9] Stephen Semmes On the nonexistence of bilipschitz parameterizations and geometric problems about A -weights, Rev. Mat. Iberoam., Volume 12 (1996) no. 2, pp. 337-410 | DOI | Zbl

Cité par Sources :

Commentaires - Politique