Quasiisometries between negatively curved Hadamard manifolds

• Autores: Xiangdong Xie
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 79, Nº 1, 2009, págs. 15-32
• Idioma: inglés
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• Resumen

  • 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.