{"title":"与域边界相关的新度量","authors":"Xingchen Song, Gendi Wang","doi":"10.1007/s40315-024-00545-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we introduce a new metric <span>\\(\\tilde{c}\\)</span> which is associated with the domain boundary for a Ptolemy space (<i>X</i>, <i>d</i>). Moreover, we study inclusion relations of <span>\\(\\tilde{c}\\)</span> metric balls and some related hyperbolic type metric balls in subdomains of <span>\\({\\mathbb {R}}^n.\\)</span> In addition, we study distortion properties of the <span>\\(\\tilde{c}\\)</span> metric under Möbius transformations of the unit ball and quasiconformality of bilipschitz mappings in the <span>\\(\\tilde{c}\\)</span> metric.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A New Metric Associated with the Domain Boundary\",\"authors\":\"Xingchen Song, Gendi Wang\",\"doi\":\"10.1007/s40315-024-00545-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we introduce a new metric <span>\\\\(\\\\tilde{c}\\\\)</span> which is associated with the domain boundary for a Ptolemy space (<i>X</i>, <i>d</i>). Moreover, we study inclusion relations of <span>\\\\(\\\\tilde{c}\\\\)</span> metric balls and some related hyperbolic type metric balls in subdomains of <span>\\\\({\\\\mathbb {R}}^n.\\\\)</span> In addition, we study distortion properties of the <span>\\\\(\\\\tilde{c}\\\\)</span> metric under Möbius transformations of the unit ball and quasiconformality of bilipschitz mappings in the <span>\\\\(\\\\tilde{c}\\\\)</span> metric.</p>\",\"PeriodicalId\":49088,\"journal\":{\"name\":\"Computational Methods and Function Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods and Function Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40315-024-00545-4\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods and Function Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00545-4","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
In this paper, we introduce a new metric \(\tilde{c}\) which is associated with the domain boundary for a Ptolemy space (X, d). Moreover, we study inclusion relations of \(\tilde{c}\) metric balls and some related hyperbolic type metric balls in subdomains of \({\mathbb {R}}^n.\) In addition, we study distortion properties of the \(\tilde{c}\) metric under Möbius transformations of the unit ball and quasiconformality of bilipschitz mappings in the \(\tilde{c}\) metric.
期刊介绍：
CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.
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