{"title":"On boundary discreteness of mappings with a modulus condition","authors":"E. Sevost’yanov","doi":"10.1007/s10474-023-01381-z","DOIUrl":null,"url":null,"abstract":"<div><p>We study the boundary behavior of spatial mappings that distort the\nmodulus of families of paths in the same way as the inverse Poletsky\ninequality. Under certain conditions on the boundaries of the\ncorresponding domains, we have shown that such mappings have a\ncontinuous boundary extension. Separately, we study the problem of\ndiscreteness of the indicated extension. It is shown that under\nsome requirements, it is light, and under some more strong\nconditions, it is discrete in the closure of a domain.\n</p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"171 1","pages":"67 - 87"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-023-01381-z","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the boundary behavior of spatial mappings that distort the
modulus of families of paths in the same way as the inverse Poletsky
inequality. Under certain conditions on the boundaries of the
corresponding domains, we have shown that such mappings have a
continuous boundary extension. Separately, we study the problem of
discreteness of the indicated extension. It is shown that under
some requirements, it is light, and under some more strong
conditions, it is discrete in the closure of a domain.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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