多个复杂变量的加权约西达映射

arXiv - MATH - Complex Variables Pub Date : 2024-08-13 DOI:arxiv-2408.06800

Nikhil Bharti, Nguyen Van Thin

{"title":"多个复杂变量的加权约西达映射","authors":"Nikhil Bharti, Nguyen Van Thin","doi":"arxiv-2408.06800","DOIUrl":null,"url":null,"abstract":"Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let\n$\\varphi: [0,\\infty)\\rightarrow (0,\\infty)$ be positive function such that\n$$\\gamma_r=\\sup\\limits_{r\\leq\na<b}\\left|(\\varphi(a)-\\varphi(b))/(a-b)\\right|\\leq C,~r\\in (0,\\infty),$$ for\nsome $C\\in (0,1],$ and $\\lim_{r\\rightarrow\\infty}\\gamma_r=0.$ A holomorphic\nmapping $f:\\mathbb{C}^{m}\\rightarrow M$ is said to be a weighted Yosida mapping\nif for any $z,~\\xi\\in\\mathbb{C}^{m}$ with $\\|\\xi\\|=1,$ the quantity\n$\\varphi(\\|z\\|)E_{M}(f(z), df(z)(\\xi))$ remains bounded above, where $df(z)$ is\nthe map from $T_z(\\mathbb{C}^{m})$ to $T_{f(z)}(M)$ induced by $f.$ We present\nseveral criteria of holomorphic mappings belonging to the class of all weighted\nYosida mappings.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"314 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weighted Yosida Mappings of Several Complex Variables\",\"authors\":\"Nikhil Bharti, Nguyen Van Thin\",\"doi\":\"arxiv-2408.06800\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let\\n$\\\\varphi: [0,\\\\infty)\\\\rightarrow (0,\\\\infty)$ be positive function such that\\n$$\\\\gamma_r=\\\\sup\\\\limits_{r\\\\leq\\na<b}\\\\left|(\\\\varphi(a)-\\\\varphi(b))/(a-b)\\\\right|\\\\leq C,~r\\\\in (0,\\\\infty),$$ for\\nsome $C\\\\in (0,1],$ and $\\\\lim_{r\\\\rightarrow\\\\infty}\\\\gamma_r=0.$ A holomorphic\\nmapping $f:\\\\mathbb{C}^{m}\\\\rightarrow M$ is said to be a weighted Yosida mapping\\nif for any $z,~\\\\xi\\\\in\\\\mathbb{C}^{m}$ with $\\\\|\\\\xi\\\\|=1,$ the quantity\\n$\\\\varphi(\\\\|z\\\\|)E_{M}(f(z), df(z)(\\\\xi))$ remains bounded above, where $df(z)$ is\\nthe map from $T_z(\\\\mathbb{C}^{m})$ to $T_{f(z)}(M)$ induced by $f.$ We present\\nseveral criteria of holomorphic mappings belonging to the class of all weighted\\nYosida mappings.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"314 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-13\",\"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-2408.06800\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.06800","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

让 $M$ 是一个度量为 $E_{M}$ 的完整复赫尔墨斯流形，并让 $\varphi：[0,\infty)\rightarrow(0,\infty)$是正函数，使得$$\gamma_r=\sup\limits_{r\leqa本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Weighted Yosida Mappings of Several Complex Variables

Let $M$ be a complete complex Hermitian manifold with metric $E_{M}$ and let $\varphi: [0,\infty)\rightarrow (0,\infty)$ be positive function such that $$\gamma_r=\sup\limits_{r\leq a

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Complex Variables

自引率

0.00%

发文量