{"title":"卡诺群上有限畸变映射的拓扑特性","authors":"D. V. Isangulova","doi":"10.1134/s0037446624010063","DOIUrl":null,"url":null,"abstract":"<p>We prove that\nevery mapping with finite distortion on a Carnot group\nis open and discrete provided that it is quasilight and the distortion coefficient is integrable.\nAlso, we estimate the Hausdorff dimension of the preimages of points\nfor mappings on a Carnot group\nwith a bounded multiplicity function\nand summable distortion coefficient.\nFurthermore, we give some example showing that\nthe obtained estimates cannot be improved.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"12 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological Properties of Mappings with Finite Distortion on Carnot Groups\",\"authors\":\"D. V. Isangulova\",\"doi\":\"10.1134/s0037446624010063\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that\\nevery mapping with finite distortion on a Carnot group\\nis open and discrete provided that it is quasilight and the distortion coefficient is integrable.\\nAlso, we estimate the Hausdorff dimension of the preimages of points\\nfor mappings on a Carnot group\\nwith a bounded multiplicity function\\nand summable distortion coefficient.\\nFurthermore, we give some example showing that\\nthe obtained estimates cannot be improved.</p>\",\"PeriodicalId\":49533,\"journal\":{\"name\":\"Siberian Mathematical Journal\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0037446624010063\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446624010063","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Topological Properties of Mappings with Finite Distortion on Carnot Groups
We prove that
every mapping with finite distortion on a Carnot group
is open and discrete provided that it is quasilight and the distortion coefficient is integrable.
Also, we estimate the Hausdorff dimension of the preimages of points
for mappings on a Carnot group
with a bounded multiplicity function
and summable distortion coefficient.
Furthermore, we give some example showing that
the obtained estimates cannot be improved.
期刊介绍：
Siberian Mathematical Journal is journal published in collaboration with the Sobolev Institute of Mathematics in Novosibirsk. The journal publishes the results of studies in various branches of mathematics.
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