Large scale geometry of negatively curved ℝn ⋊ ℝ

Xie, Xiangdong¹

¹ Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA

Geometry & topology, Tome 18 (2014) no. 2, pp. 831-872.

Résumé

We classify all negatively curved ${ℝ}^n⋊ℝ$ up to quasi-isometry. We show that all quasi-isometries between such manifolds (except when they are bilipschitz to the real hyperbolic spaces) are almost similarities. We prove these results by studying the quasisymmetric maps on the ideal boundary of these manifolds.

Détail

DOI : 10.2140/gt.2014.18.831

Classification : 20F65, 30C65, 53C20
Keywords: quasiisometry, quasisymmetric map, negatively curved solvable Lie groups

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