Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings

Antoine Clais. "Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings." Analysis and Geometry in Metric Spaces 4.1 (2016): 1-53, electronic only. <http://eudml.org/doc/276717>.

@article{AntoineClais2016,
abstract = {In this article, we discuss the quasiconformal structure of boundaries of right-angled hyperbolic buildings using combinatorial tools. In particular, we exhibit some examples of buildings of dimension 3 and 4 whose boundaries satisfy the combinatorial Loewner property. This property is a weak version of the Loewner property. This is motivated by the fact that the quasiconformal structure of the boundary led to many results of rigidity in hyperbolic spaces since G.D.Mostow. In the case of buildings of dimension 2, many work have been done by M. Bourdon and H. Pajot. In particular, the Loewner property on the boundary permitted them to prove the quasi-isometry rigidity of right-angled Fuchsian buildings.},
author = {Antoine Clais},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Boundary of hyperbolic space; building; combinatorial modulus; combinatorial Loewner property; quasi-conformal analysis; boundary of hyperbolic space},
language = {eng},
number = {1},
pages = {1-53, electronic only},
title = {Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings},
url = {http://eudml.org/doc/276717},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Antoine Clais
TI - Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings
JO - Analysis and Geometry in Metric Spaces
PY - 2016
VL - 4
IS - 1
SP - 1
EP - 53, electronic only
AB - In this article, we discuss the quasiconformal structure of boundaries of right-angled hyperbolic buildings using combinatorial tools. In particular, we exhibit some examples of buildings of dimension 3 and 4 whose boundaries satisfy the combinatorial Loewner property. This property is a weak version of the Loewner property. This is motivated by the fact that the quasiconformal structure of the boundary led to many results of rigidity in hyperbolic spaces since G.D.Mostow. In the case of buildings of dimension 2, many work have been done by M. Bourdon and H. Pajot. In particular, the Loewner property on the boundary permitted them to prove the quasi-isometry rigidity of right-angled Fuchsian buildings.
LA - eng
KW - Boundary of hyperbolic space; building; combinatorial modulus; combinatorial Loewner property; quasi-conformal analysis; boundary of hyperbolic space
UR - http://eudml.org/doc/276717
ER -