Hölder conditions for endomorphisms of hyperbolic groups

Abstract

It is proved that an endomorphism $\phi$ of a hyperbolic group $G$ satisfies a Hölder condition with respect to a visual metric if and only if $\phi$ is virtually injective and $G\phi$ is a quasiconvex subgroup of $G$. If $G$ is virtually free or torsion-free co-hopfian, then $\phi$ is uniformly continuous if and only if it it satisfies a Hölder condition if and only if it is virtually injective. Lipschitz conditions are discussed for free group automorphisms.

27 pages

References in corpus (1)

• Geometric characterizations of virtually free groups