Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Poincaré inequalities and quasiconformal structure on the boundary of some hyperbolic buildings

Authors:	Marc Bourdon Hervé Pajot

Affiliation:	Institut Elie Cartan, Département de mathématiques, Université de Nancy I, BP 239, 54506 Vandoeuvre les Nancy, France ; Mathematical Science Research Institute, 1000 Centennial Drive, Berkeley, California 94720-5070

Abstract:	In this paper we shall show that the boundary $partial I_{p,q}$ of the hyperbolic building $I_{p,q}$ considered by M. Bourdon admits Poincaré type inequalities. Then by using Heinonen-Koskela's work, we shall prove Loewner capacity estimates for some families of curves of $partial I_{p,q}$ and the fact that every quasiconformal homeomorphism $f : partial I_{p,q} longrightarrow partial I_{p,q}$ is quasisymmetric. Therefore by these results, the answer to questions 19 and 20 of Heinonen and Semmes (Thirty-three YES or NO questions about mappings, measures and metrics, Conform Geom. Dyn. 1 (1997), 1-12) is NO.

Keywords:	Hyperbolic building Poincar'e inequality quasiconformal mapping

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文