{"paper":{"title":"On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Open and discrete mappings from Orlicz-Sobolev classes admit continuous extensions to prime ends even without preserving the domain boundary.","cross_cats":[],"primary_cat":"math.CV","authors_text":"Evgeny Sevost'yanov, Zarina Kovba","submitted_at":"2026-04-16T13:55:27Z","abstract_excerpt":"We study problems related to continuous boundary extension of mappings of Orlicz-Sobolev classes in terms of prime ends. The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the boundary of a domain). These results generalize the well-known results of Caratheodory on boundary extension of conformal mappings."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the boundary of a domain). These results generalize the well-known results of Caratheodory on boundary extension of conformal mappings.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The mappings are assumed to belong to suitable Orlicz-Sobolev classes and to be open and discrete (but not closed), with the underlying domain admitting a prime-end compactification.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves prime-end boundary extensions for open discrete unclosed mappings in Orlicz-Sobolev classes, extending Carathéodory's theorem.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Open and discrete mappings from Orlicz-Sobolev classes admit continuous extensions to prime ends even without preserving the domain boundary.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7c86b3823a7fb278559048f52b688f8d7297b773e04af65cf654f957af9ee2d4"},"source":{"id":"2604.15026","kind":"arxiv","version":2},"verdict":{"id":"e1742590-e648-4b4b-9614-b2dd0c9251df","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T17:24:44.057013Z","strongest_claim":"The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the boundary of a domain). These results generalize the well-known results of Caratheodory on boundary extension of conformal mappings.","one_line_summary":"Proves prime-end boundary extensions for open discrete unclosed mappings in Orlicz-Sobolev classes, extending Carathéodory's theorem.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The mappings are assumed to belong to suitable Orlicz-Sobolev classes and to be open and discrete (but not closed), with the underlying domain admitting a prime-end compactification.","pith_extraction_headline":"Open and discrete mappings from Orlicz-Sobolev classes admit continuous extensions to prime ends even without preserving the domain boundary."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.15026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":29,"sample":[{"doi":"","year":2019,"title":"- Analysis and Mathematical Physics 9:4, 2019, 1941-1975","work_id":"0675a514-6596-4f19-b6f5-f537940a1975","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1913,"title":"Uber die Begrenzung der einfachzusammenh\\","work_id":"ebff4b90-356d-4698-8c1f-da62e528b251","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1966,"title":"Collingwood, E.F. and A.J. 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