{"paper":{"title":"Equicontinuity and normality of mappings with integrally bounded $p$-moduli","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anatoly Golberg, Evgeny Sevost'yanov, Ruslan Salimov","submitted_at":"2013-09-07T06:13:43Z","abstract_excerpt":"We consider the generic discrete open mappings in ${\\mathbb R}^n$ under which the perturbation of extremal lengths of curve collections is controlled integrally via $\\int Q(x)\\eta^p(|x-x_0|) dm(x)$ with $n-1<p<n$, where $Q$ is a measurable function on ${\\mathbb R}^n$ and $\\int\\limits_{r_1}^{r_2} \\eta(r) dr \\ge 1$ for any $\\eta$ on a given interval $[r_1,r_2].$ We proved that the family of all open discrete mappings of above type is normal under appropriate restrictions on the majorant $Q.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1826","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"}