# Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings

Analysis and Geometry in Metric Spaces (2016)

- Volume: 4, Issue: 1, page 1-53, electronic only
- ISSN: 2299-3274

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topAntoine 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 -

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