{"paper":{"title":"Analog of Montel theorem for mappings of Sobolev class with finite distortion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Evgeny Sevost'yanov","submitted_at":"2014-04-18T22:28:35Z","abstract_excerpt":"The present paper is devoted to the study of classes of mappings with non-bounded characteristic of quasiconformality. It is obtained a result on normal families of the open discrete mappings $f:D\\rightarrow {\\Bbb C}\\setminus\\{a, b\\}$ of the class $W_{loc}^{1, 1}$ having a finite distortion and omitting two fixed values $a\\ne b$ in ${\\Bbb C},$ maximal dilatations of which has a majorant of the class of finite mean oscillation at every point. In particular, the result mentioned above holds for the so-called $Q$-mappings and is an analog of known Montel theorem for analytic functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4896","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"}