{"paper":{"title":"On boundary behavior of spatial mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Denis Kovtonyuk, Vladimir Ryazanov","submitted_at":"2014-08-03T08:05:32Z","abstract_excerpt":"We show that homeomorphisms $f$ in ${\\Bbb R}^n$, $n\\geqslant3$, of finite distortion in the Orlicz--Sobolev classes $W^{1,\\varphi}_{\\rm loc}$ with a condition on $\\varphi$ of the Calderon type and, in particular, in the Sobolev classes $W^{1,p}_{\\rm loc}$ for $p>n-1$ are the so-called lower $Q$-homeomorphisms, $Q(x)=K^{\\frac{1}{n-1}}_I(x,f)$, where $K_I(x,f)$ is its inner dilatation. The statement is valid also for all finitely bi-Lipschitz mappings that a far--reaching extension of the well-known classes of isometric and quasiisometric mappings. This makes pos\\-sib\\-le to apply our theory of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0470","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"}