Abstract
We prove a generalization of the fellow traveller property for a certain type of quasi-geodesics and use it to present three equivalent geometric formulations of the bounded reduction property and to prove that this is equivalent to preservation of a coarse median. We then provide an affirmative answer to a question from Araújo and Silva as to whether every nontrivial uniformly continuous endomorphism of a hyperbolic group with respect to a visual metric satisfies a Hölder condition. We remark that these results combined with the work done by Paulin prove that every endomorphism admitting a continuous extension to the completion has a finitely generated fixed point subgroup.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
