{"paper":{"title":"The Miniowitz and Vuorinen theorems for the mappings with non-bounded characteristics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Evgeny Sevost'yanov","submitted_at":"2012-11-26T01:27:05Z","abstract_excerpt":"The present paper is devoted to the study of classes of mappings with non--bounded characteristics of quasiconformality. It is proved that the normal families of mappings distorting the families of mappings in ${\\Bbb R}^n$ by special way, have the logarithmic order of growth in the neighborhood of every point. There are proved some sufficient conditions of normality of such mappings $f:D\\rightarrow \\bar{{\\Bbb R}^n},$ $n\\ge 2,$ omitting the values of some set $E_f$ with some constraints of the type $c(E_f)\\ge \\delta,$ $\\delta\\in {\\Bbb R},$ where $c(\\cdot)$ is the special set function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5834","kind":"arxiv","version":6},"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"}