Divergence of Morse geodesics

Abstract

Behrstock and Druţu raised a question about the existence of Morse geodesics in $CAT(0)$ spaces with divergence function strictly greater than $r^n$ and strictly less than $r^{n+1}$, where $n$ is an integer greater than $1$. In this paper, we answer the question of Behrstock and Druţu by showing that for each real number $s\ge 2$, there is a $CAT(0)$ space $X$ with a proper and cocompact action of some finitely generated group such that $X$ contains a Morse bi-infinite geodesic with the divergence equivalent to $r^s$.

References in corpus (3)

• Contracting Boundaries of CAT(0) Spaces
• On metric relative hyperbolicity
• Relative divergence of finitely generated groups

Cited by in corpus (3)

• On strongly quasiconvex subgroups
• Morse geodesics in torsion groups
• Divergence spectra and Morse boundaries of relatively hyperbolic groups