no. 7
Geometry/Group theory
Conformal dimension on boundary of right-angled hyperbolic buildings
[Dimension conforme du bord d'un immeuble hyperbolique à angles droits]

Présenté par : the Editorial Board

Clais, Antoine1
1 Technion, Department of Mathematics, 32000 Haifa, Israel
Comptes Rendus. Mathématique, Tome 355 (2017) no. 7, pp. 819-823.

Dans cette note, on utilise des modules combinatoires sur le bord d'un immeuble hyperbolique à angles droits pour encadrer sa dimension conforme. La borne inférieure obtenue est optimale dans le cas des immeubles fuchsiens.

In this note, we use some combinatorial modulus on the boundary of a right-angled hyperbolic building to control its conformal dimension. The lower bound obtained is optimal in the case of Fuchsian buildings.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.06.006
Clais, Antoine 1

1 Technion, Department of Mathematics, 32000 Haifa, Israel 
@article{CRMATH_2017__355_7_819_0,
     author = {Clais, Antoine},
     title = {Conformal dimension on boundary of right-angled hyperbolic buildings},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {819--823},
     publisher = {Elsevier},
     volume = {355},
     number = {7},
     year = {2017},
     doi = {10.1016/j.crma.2017.06.006},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2017.06.006/}
}
TY  - JOUR
AU  - Clais, Antoine
TI  - Conformal dimension on boundary of right-angled hyperbolic buildings
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 819
EP  - 823
VL  - 355
IS  - 7
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2017.06.006/
DO  - 10.1016/j.crma.2017.06.006
LA  - en
ID  - CRMATH_2017__355_7_819_0
ER  - 
%0 Journal Article
%A Clais, Antoine
%T Conformal dimension on boundary of right-angled hyperbolic buildings
%J Comptes Rendus. Mathématique
%D 2017
%P 819-823
%V 355
%N 7
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2017.06.006/
%R 10.1016/j.crma.2017.06.006
%G en
%F CRMATH_2017__355_7_819_0
Clais, Antoine. Conformal dimension on boundary of right-angled hyperbolic buildings. Comptes Rendus. Mathématique, Tome 355 (2017) no. 7, pp. 819-823. doi : 10.1016/j.crma.2017.06.006. http://www.numdam.org/articles/10.1016/j.crma.2017.06.006/

[1] Bonk, M.; Kleiner, B. Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary, Geom. Topol., Volume 9 (2005), pp. 219-246

[2] Bourdon, M. Immeubles hyperboliques, dimension conforme et rigidité de Mostow, Geom. Funct. Anal., Volume 7 (1997), pp. 245-268

[3] Bourdon, M.; Kleiner, B. Combinatorial modulus, the combinatorial Loewner property, and Coxeter groups, Groups Geom. Dyn., Volume 7 (2013), pp. 39-107

[4] Carrasco Piaggio, M. On the conformal gauge of a compact metric space, Ann. Sci. Éc. Norm. Supér. (4), Volume 46 (2013), pp. 495-548

[5] Clais, A. Combinatorial modulus on boundary of Right–Angled hyperbolic buildings, Anal. Geom. Metr. Spaces, Volume 4 (2016) no. 1

[6] Davis, M. The Geometry and Topology of Coxeter Groups, Princeton University Press, Princeton, NJ, USA, 2008

[7] Davis, M.; Meier, J. The topology at infinity of Coxeter groups and buildings, Comment. Math. Helv., Volume 77 (2002), pp. 746-766

[8] Haïssinsky, P. Géométrie quasiconforme, analyse au bord des espaces métriques hyperboliques et rigidités [d'après Mostow, Pansu, Bourdon, Pajot, Bonk, Kleiner…], Astérisque, Volume 2007/2008 (2009)

[9] Kleiner, B. The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity, International Congress of Mathematicians. Vol. II, 2006, pp. 743-768

[10] Mackay, J.; Tyson, J. Conformal Dimension, American Mathematical Society, Providence, RI, USA, 2010

[11] Meier, J. When is the graph product of hyperbolic groups hyperbolic?, Geom. Dedic., Volume 61 (1996), pp. 29-41

[12] Pansu, P. Dimension conforme et sphère à l'infini des variétés à courbure négative, Ann. Acad. Sci. Fenn., Ser. A I Math., Volume 14 (1989), pp. 177-212

Cité par Sources :