{"title":"The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B p n of ℂn","authors":"","doi":"10.1007/s10473-024-0304-y","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit <em>p</em>-ball <em>B</em><span> <sub><em>p</em></sub> <sup><em>n</em></sup> </span> of ℂ<sup><em>n</em></sup>. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on <em>B</em><span> <sub><em>p</em></sub> <sup><em>n</em></sup> </span> is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for <em>p</em> = 2, and the unit polydisk for <em>p</em> = ∞, respectively.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0304-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball Bpn of ℂn. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on Bpn is obtained. These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p = 2, and the unit polydisk for p = ∞, respectively.
摘要 通过引入 Carathéodory 度量，我们建立了ℂn 的单位 p 球 B p n 上全形自映射的边界施瓦茨 Lemma。此外，我们还得到了定义在 B p n 上的全形自映射的边界刚性定理。这些结果分别涵盖了 p = 2 时单位球上的全形自贴图的边界施瓦茨 Lewarz Lemma 和刚性结果，以及 p = ∞ 时单位多盘上的全形自贴图的边界刚性结果。
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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