Weighted Yosida Mappings of Several Complex Variables

Nikhil Bharti, Nguyen Van Thin
{"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}
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Abstract

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 $$\gamma_r=\sup\limits_{r\leq a
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多个复杂变量的加权约西达映射
让 $M$ 是一个度量为 $E_{M}$ 的完整复赫尔墨斯流形,并让 $\varphi:[0,\infty)\rightarrow(0,\infty)$是正函数,使得$$\gamma_r=\sup\limits_{r\leqa
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