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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access February 11, 2016

Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings

  • Antoine Clais


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.


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Received: 2015-3-31
Accepted: 2016-1-16
Published Online: 2016-2-11

© 2016 Antoine Clais

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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