Seminar| Institute of Mathematical Sciences
Time: Thursday, July 2th, 2026,16:00-17:00
Location: IMS RS506
Speaker: Xiangdong Xie, Bowling Green State University
Abstract:A group of quasiconformal maps of a metric space X is called a uniform quasiconformal group if there is some K at least one such that each element of the group is K-quasiconformal. Clearly a quasiconformal conjugate of a conformal group is a uniform quasiconformal group. A natural question is when the converse holds. Tukia's theorem says that if a uniform quasiconformal group of the n-sphere for n at least 2 is big enough, then the converse holds. We present a generalization of Tukia's theorem to uniform quasiconformal groups of two classes of nilpotent Lie groups: Carnot groups and Carnot-by-Carnot groups. This has consequences for the quasiisometric rigidity of solvable Lie groups and finitely generated solvable groups. This talk is based on joint work with Tullia Dymarz and David Fisher.