Resumen de Quasiisometries between negatively curved Hadamard manifolds

Xiangdong Xie

• Let H1, H2 be the universal covers of two compact Riemannian manifolds (of dimension not equal to 4) with negative sectional curvature. Then every quasiisometry between them lies at a finite distance from a bilipschitz homeomorphism. As a consequence, every self-quasiconformal map of a Heisenberg group (equipped with the Carnot metric and viewed as the ideal boundary of complex hyperbolic space) of dimension at least 5 extends to a self-quasiconformal map of the complex hyperbolic space.