Evgeny Sevost'yanov, Victoria Desyatka Zarina Kovba
{"title":"On the prime ends extension of unclosed inverse mappings","authors":"Evgeny Sevost'yanov, Victoria Desyatka Zarina Kovba","doi":"arxiv-2409.02956","DOIUrl":null,"url":null,"abstract":"We consider mappings that distort the modulus of families of paths in the\nopposite direction in the manner of Poletsky's inequality. Here we study the\ncase when the mappings are not closed, in particular, they do not preserve the\nboundary of the domain under the mapping. Under certain conditions, we obtain\nresults on the continuous boundary extension of such mappings in the sense of\nprime ends. In addition, we obtain corresponding results on the equicontinuity\nof families of such mappings in terms of prime ends.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"178 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02956","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider mappings that distort the modulus of families of paths in the
opposite direction in the manner of Poletsky's inequality. Here we study the
case when the mappings are not closed, in particular, they do not preserve the
boundary of the domain under the mapping. Under certain conditions, we obtain
results on the continuous boundary extension of such mappings in the sense of
prime ends. In addition, we obtain corresponding results on the equicontinuity
of families of such mappings in terms of prime ends.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
