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Analysis and Geometry in Metric Spaces

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Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings

Antoine Clais
Published Online: 2016-02-11 | DOI: https://doi.org/10.1515/agms-2016-0001


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.

Keywords: Boundary of hyperbolic space; building; combinatorial modulus; combinatorial Loewner property; quasi-conformal analysis


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About the article

Received: 2015-03-31

Accepted: 2016-01-16

Published Online: 2016-02-11

Citation Information: Analysis and Geometry in Metric Spaces, Volume 4, Issue 1, ISSN (Online) 2299-3274, DOI: https://doi.org/10.1515/agms-2016-0001.

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© 2016 Antoine Clais. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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