A quantitative version of the Morse lemma and ideal boundary fixing quasiisometries

Abstract

The article is devoted to a proof of the optimal upper-bound for Morse Lemma, its "anti"-version and their applications. Roughly speaking, Morse Lemma states that in a hyperbolic metric space, a $\lambda$-quasi-geodesic $\gamma$ sits in a ${\lambda }^2$-neighborhood of every geodesic $\sigma$ with same endpoints. Anti-Morse Lemma states that $\sigma$ sits in a $\log \lambda$-neighborhood of $\gamma$. Applications include the displacement of points under quasi-isometries fixing the ideal boundary.

Cited by in corpus (3)

• A combination theorem for Anosov subgroups
• Large-scale sublinearly Lipschitz geometry of hyperbolic spaces
• A corrected quantitative version of the Morse lemma