Combinatorial Modulus on Boundary of Right-Angled Hyperbolic Buildings

• Autorzy: Antoine Clais
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Analysis and Geometry in Metric Spaces
• Rocznik: 2016
• Tom: 4
• Numer: 1

Daty

otrzymano

2015-03-31

zaakceptowano

2016-01-16

online

2016-02-11

Twórcy

autor

Antoine Clais

• Laboratoire Paul Painlevé, Université Lille 1, 59655 Villeneuve d’Ascq, France

Identyfikatory

DOI

10.1515/agms-2016-0001