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Mathematics > Group Theory

arXiv:1405.6310 (math)
[Submitted on 24 May 2014 (v1), last revised 21 Sep 2014 (this version, v3)]

Title:Hölder conditions for endomorphisms of hyperbolic groups

Authors:Vítor Araújo, Pedro V. Silva
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Abstract:It is proved that an endomorphism $\varphi$ of a hyperbolic group $G$ satisfies a Hölder condition with respect to a visual metric if and only if $\varphi$ is virtually injective and $G\varphi$ is a quasiconvex subgroup of $G$. If $G$ is virtually free or torsion-free co-hopfian, then $\varphi$ 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.
Comments: 27 pages
Subjects: Group Theory (math.GR); Metric Geometry (math.MG)
MSC classes: 20F67, 20E36, 51M10
Cite as: arXiv:1405.6310 [math.GR]
  (or arXiv:1405.6310v3 [math.GR] for this version)
  https://doi.org/10.48550/arXiv.1405.6310
Journal reference: Communications in Algebra, 44:10, 4483-4503 (2016)
Related DOI: https://doi.org/10.1080/00927872.2015.1094480

Submission history

From: Pedro V. Silva [view email]
[v1] Sat, 24 May 2014 15:23:01 UTC (25 KB)
[v2] Sat, 31 May 2014 22:31:00 UTC (26 KB)
[v3] Sun, 21 Sep 2014 12:43:33 UTC (28 KB)
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