{"title":"剪切映射和单位球的Runge映射，不嵌入到范围为Cn的Loewner链中","authors":"Filippo Bracci, P. Gumenyuk","doi":"10.24193/subbmath.2022.2.03","DOIUrl":null,"url":null,"abstract":"In this paper we study the class of ``shearing'' holomorphic maps of the unit ball of the form $(z,w)\\mapsto (z+g(w), w)$. Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in $\\C^n$ which however cannot be embedded into a Loewner chain whose range is $\\C^n$.","PeriodicalId":30022,"journal":{"name":"Studia Universitatis BabesBolyai Geologia","volume":"133 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range Cn\",\"authors\":\"Filippo Bracci, P. Gumenyuk\",\"doi\":\"10.24193/subbmath.2022.2.03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we study the class of ``shearing'' holomorphic maps of the unit ball of the form $(z,w)\\\\mapsto (z+g(w), w)$. Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in $\\\\C^n$ which however cannot be embedded into a Loewner chain whose range is $\\\\C^n$.\",\"PeriodicalId\":30022,\"journal\":{\"name\":\"Studia Universitatis BabesBolyai Geologia\",\"volume\":\"133 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Universitatis BabesBolyai Geologia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24193/subbmath.2022.2.03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Universitatis BabesBolyai Geologia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24193/subbmath.2022.2.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range Cn
In this paper we study the class of ``shearing'' holomorphic maps of the unit ball of the form $(z,w)\mapsto (z+g(w), w)$. Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in $\C^n$ which however cannot be embedded into a Loewner chain whose range is $\C^n$.
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