{"paper":{"title":"Absolute continuity on paths of spatial open discrete mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anatoly Golberg, Evgeny Sevost'yanov","submitted_at":"2015-04-21T11:00:58Z","abstract_excerpt":"We prove that open discrete mappings of Sobolev classes $W_{\\rm loc}^{1, p},$ $p>n-1,$ with locally integrable inner dilatations admit $ACP_p^{\\,-1}$-property, which means that these mappings are absolutely continuous on almost all preimage paths with respect to $p$-module. In particular, our results extend the well-known Poletski\\u\\i\\ lemma for quasiregular mappings. We also establish the upper bounds for $p$-module of such mappings in terms of integrals depending on the inner dilatations and arbitrary admissible functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05385","kind":"arxiv","version":1},"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"}