{"paper":{"title":"H\\\"older conditions for endomorphisms of hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.GR","authors_text":"Pedro V. Silva, V\\'itor Ara\\'ujo","submitted_at":"2014-05-24T15:23:01Z","abstract_excerpt":"It is proved that an endomorphism $\\varphi$ of a hyperbolic group $G$ satisfies a H\\\"older 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 H\\\"older condition if and only if it is virtually injective. Lipschitz conditions are discussed for free group automorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6310","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}