{"title":"拟亚纯映射的图形极限与四分体特征的畸变","authors":"V. V. Aseev","doi":"10.1134/s0037446623060034","DOIUrl":null,"url":null,"abstract":"<p>We fully describe\nthe form of\nthe graphical limit of a sequence of <span>\\( K \\)</span>-quasimeromorphic mappings\nof a domain <span>\\( D \\)</span>\nin <span>\\( \\overline{R^{n}} \\)</span>\nwhich take each of its values\nat <span>\\( N \\)</span>\ndistinct points at most.\nFor the family of all <span>\\( K \\)</span>-quasimeromorphic mappings of <span>\\( \\overline{R^{n}} \\)</span>\nonto itself\ntaking each value at <span>\\( N \\)</span> points at most\nwe establish the presence of a common estimate for the distortion of\nthe Ptolemaic characteristic of generalized tetrads\n(quadruples of disjoint compact sets).</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads\",\"authors\":\"V. V. Aseev\",\"doi\":\"10.1134/s0037446623060034\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We fully describe\\nthe form of\\nthe graphical limit of a sequence of <span>\\\\( K \\\\)</span>-quasimeromorphic mappings\\nof a domain <span>\\\\( D \\\\)</span>\\nin <span>\\\\( \\\\overline{R^{n}} \\\\)</span>\\nwhich take each of its values\\nat <span>\\\\( N \\\\)</span>\\ndistinct points at most.\\nFor the family of all <span>\\\\( K \\\\)</span>-quasimeromorphic mappings of <span>\\\\( \\\\overline{R^{n}} \\\\)</span>\\nonto itself\\ntaking each value at <span>\\\\( N \\\\)</span> points at most\\nwe establish the presence of a common estimate for the distortion of\\nthe Ptolemaic characteristic of generalized tetrads\\n(quadruples of disjoint compact sets).</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0037446623060034\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446623060034","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们充分描述了在\( \overline{R^{n}} \)域\( D \)上的一组\( K \) -拟亚纯映射序列的图形极限形式,这些序列的每个值最多取\( N \)个不同的点。对于\( \overline{R^{n}} \)到自身的所有\( K \) -拟亚纯映射族(最多取\( N \)点上的每个值),我们建立了广义四分体(不相交紧集的四重组)托勒密特征畸变的一个公共估计的存在性。
Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads
We fully describe
the form of
the graphical limit of a sequence of \( K \)-quasimeromorphic mappings
of a domain \( D \)
in \( \overline{R^{n}} \)
which take each of its values
at \( N \)
distinct points at most.
For the family of all \( K \)-quasimeromorphic mappings of \( \overline{R^{n}} \)
onto itself
taking each value at \( N \) points at most
we establish the presence of a common estimate for the distortion of
the Ptolemaic characteristic of generalized tetrads
(quadruples of disjoint compact sets).