Xiangdong Xie

Professor

Phone: 419-372-8317
Email: xiex@bgsu.edu
Address: Office: 425 Mitchell B. McLeod Hall
Department of Mathematics and Statistics
Bowling Green State University
Bowling Green, OH 43403-0206

Research Interests

• Geometry and Topology
• Geometric Analysis

Publications

(with Tullia Dymarz) Day's fixed point theorem, group cohomology and quasiisometric rigidity -- accepted by Groups, Geometry and Dynamics

(with Enrico Le Donne) Rigidity of fiber-preserving quasisymmetric maps  -- accepted by Revista Matematica Iberoamericana

Quasiconformal maps on non-rigid Carnot groups -- submitted

Rigidity of quasiconformal maps on Carnot groups -- submitted

(with Mike Hughes and Mihai Staic) Classification of a class of nonrigid Carnot groups  -- Journal of Lie Theory 25 (2015), No. 3, 717 -- 732.

Quasiconformal maps on model Filiform groups -- Michigan Mathematical Journal 64 (2015), no.1, 169 -- 202.

Rigidity of quasiisometries of HMN associated with non-diagonalizable derivation of the Heisenberg algebra -- to appear in Quarterly Journal of Mathematics

Quasiisometries of negatively curved homogeneous manifolds associated with Heisenberg groups  -- Journal of Topology 8 (2015), no.1, 247--266.

Some examples of quasiisometries of nilpotent Lie  groups  -- to appear in Crelle's Journal

Large scale geometry of negatively curved  $R^n\rtimes   R$  -- Geometry and Topology 18 (2014), no. 2, 831-–872.

Quasisymmetric maps on reducible Carnot groups -- Pacific Journal of Mathematics 265 (2013), no. 1, 113–122.

Quasisymmetric maps on the ideal boundary of a negatively curved solvable Lie group -- Math. Ann. 353 (2012), no. 3, 727–746.

(with N. Shanmugalingam) A rigidity property of some negatively curved solvable Lie groups --Comment. Math. Helv. 87 (2012), no. 4, 805–823.

Quasiisometries between negatively curved Hadamard manifolds--Journal of LMS (2) 79 (2009), no. 1, 15-32.

A Bowen type rigidity theorem for non-cocompact hyperbolic groups--Math. Z. 259 (2008), no. 2, 249--253.

Nagata dimension and quasimobius maps -- Conform. Geom. Dyn. 12 (2008), 1--9.

(with D. Herron, N. Shanmugalingam) Uniformity from Gromov hyperbolicity --Illinois journal of math. 52 (2008), no.4, 1065-1109.

(with S. Buckley, D. Herron) Metric inversions and quasihyperbolic geometry --Indiana Univ. Math. J. 57 (2008), no. 2, 837--890.

Quasimobius maps preserve uniform domains --Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 2, 481--495.

Growth of relatively hyperbolic groups -- Proc. Amer. Math. Soc. 135 (2007), 695-704.

Quasi-isometric rigidity of Fuchsian buildings -- Topology 45 (2006) 101--169.

The Tits boundary of a CAT(0) $2$-complex --- Transactions of AMS 357 (2005), no. 4, 1627--1661.

Groups acting on CAT(0) square complexes --- Geometrae Dedicata 109 (2004), 59--88.

Foldable cubical complexes of nonpositive curvature --- Algebraic and Geometric Topology 4 (2004), 603--622.

(with B.Apanasov) Discrete actions on nilpotent Lie groups and negatively curved spaces---Differential Geom. Appl. 20 (2004), no. 1, 11--29

Tits alternative for closed real analytic $4$-manifolds of nonpositive curvature --- Topology and its applications 136 (2004), 87--121.

(with B.Apanasov) Manifolds of Negative Curvature and Nilpotent Groups --Topics in Complex Analysis, Differential Geometry and Mathematical Physics (1996).

(with B.Apanasov) Geometrically Finite Complex Hyperbolic Manifolds-- Internat. J. Math. 8 (1997), no. 6, 703--757