14 citations · 69 across the 29 of their papers we have counts for
15 papers · 1 filter
A Tukia-type theorem for nilpotent Lie groups and quasi-isometric rigidity of solvable groups
Tullia Dymarz, David Fisher, Xiangdong Xie
In this paper we study uniform quasiconformal groups of Carnot-by-Carnot groups. We show that they can be conjugated into conformal groups provided the induced action on the space…
Rough similarity of left-invariant Riemannian metrics on some Lie groups
Enrico Le Donne, Gabriel Pallier, Xiangdong Xie
We consider Lie groups that are either Heintze groups or Sol-type groups, which generalize the three-dimensional Lie group SOL. We prove that all left-invariant Riemannian metrics…
Quasi-isometric rigidity of a class of right-angled Coxeter groups
Jordan Bounds, Xiangdong Xie
We establish quasi-isometric rigidity for a class of right-angled Coxeter groups. Let be joins of finite generalized thick -gons with . We show that the corre…
Day's fixed point theorem, Group cohomology and Quasi-isometric rigidity
Tullia Dymarz, Xiangdong Xie
In this note we explain how Day's fixed point theorem can be used to conjugate certain groups of biLipschitz maps of a metric space into special subgroups like similarity groups. I…
Quasiisometries of negatively curved homogeneous manifolds associated with Heisenberg groups
Xiangdong Xie
We study quasiisometries between negatively curved homogeneous manifolds associated with diagonalizable derivations on Heisenberg algebras. We classify these manifolds up to quasii…
Some examples of quasiisometries of nilpotent Lie groups
Xiangdong Xie
We construct quasiisometries of nilpotent Lie groups. In particular, for any simply connected nilpotent Lie group N, we construct quasiisometries from N to itself that is not at fi…
A Rigidity Property of Some Negatively Curved Solvable Lie Groups
Nageswari Shanmugalingam, Xiangdong Xie
We show that for some negatively curved solvable Lie groups, all self quasiisometries are almost isometries. We prove this by showing that all self quasisymmetric maps of the ideal…
Quasisymmetric Maps on the Boundary of a Negatively Curved Solvable Lie Group
Xiangdong Xie
We describe all the self quasisymmetric maps on the ideal boundary of a particular negatively curved solvable Lie group. As applications, we prove a Liouville type theorem, and der…
Large scale geometry of negatively curved
Xiangdong Xie
We classify all negatively curved up to quasiisometry. We show that all quasiisometries between such manifolds (except when they are biLipschitz to the real hyper…
Quasiisometries between negatively curved Hadamard manifolds
Xiangdong Xie
Let X, Y be the universal covers of two compact Riemannian manifolds (with dimension not equal to 4) with negative sectional curvature. Then every quasiisometry between them lies a…
Growth of relatively hyperbolic groups
Xiangdong Xie
We show that a relatively hyperbolic group either is virtually cyclic or has uniform exponential growth.
Mostow rigidity for Fuchsian buildings
Xiangdong Xie
We show that if a homeomorphism between the ideal boundaries of two Fuchsian buildings preserves the combinatorial cross ratio almost everywhere, then it extends to an isomorphism…
Tits boundary of CAT(0) 2-complexes
Xiangdong Xie
We investigate the Tits boundary of locally compact CAT(0) 2-complexes. In particular we show that away from the endpoints, a geodesic segment in the Tits boundary is the ideal bou…
Tits alternative for closed real analytic 4-manifolds of nonpositive curvature
Xiangdong Xie
We study subgroups of fundamental groups of real analytic closed 4-manifolds with nonpositive sectional curvature. In particular, we are interested in the following question: if a…
Groups acting on CAT(0) square complexes
Xiangdong Xie
We study groups acting on CAT(0) square complexes. In particular we show if Y is a nonpositively curved (in the sense of A. D. Alexandrov) finite square complex and the vertex link…