Burns-Krantz rigidity in non-smooth domains

Włodzimierz Zwonek
{"title":"Burns-Krantz rigidity in non-smooth domains","authors":"Włodzimierz Zwonek","doi":"arxiv-2409.10700","DOIUrl":null,"url":null,"abstract":"Motivated by recent papers \\cite{For-Rong 2021} and \\cite{Ng-Rong 2024} we\nprove a boundary Schwarz lemma (Burns-Krantz rigidity type theorem) for\nnon-smooth boundary points of the polydisc and symmetrized bidisc. Basic tool\nin the proofs is the phenomenon of invariance of complex geodesics (and their\nleft inverses) being somehow regular at the boundary point under the mapping\nsatisfying the property as in the Burns-Krantz rigidity theorem that lets the\nproblem reduce to one dimensional problem. Additionally, we make a discussion\non bounded symmetric domains and suggest a way to prove the Burns-Krantz\nrigidity type theorem in these domains that however cannot be applied for all\nbounded symmetric domains.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"119 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","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-2409.10700","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

Motivated by recent papers \cite{For-Rong 2021} and \cite{Ng-Rong 2024} we prove a boundary Schwarz lemma (Burns-Krantz rigidity type theorem) for non-smooth boundary points of the polydisc and symmetrized bidisc. Basic tool in the proofs is the phenomenon of invariance of complex geodesics (and their left inverses) being somehow regular at the boundary point under the mapping satisfying the property as in the Burns-Krantz rigidity theorem that lets the problem reduce to one dimensional problem. Additionally, we make a discussion on bounded symmetric domains and suggest a way to prove the Burns-Krantz rigidity type theorem in these domains that however cannot be applied for all bounded symmetric domains.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
非光滑域中的伯恩斯-克兰兹刚度
受近期论文(cite{For-Rong 2021}和(cite{Ng-Rong 2024})的启发,我们证明了多圆盘和对称双圆盘非光滑边界点的边界施瓦茨定理(Burns-Krantz rigidity type theorem)。证明的基本工具是在满足伯恩斯-克兰茨刚性定理属性的映射下,复大地线(及其左反函数)在边界点处具有某种规则性,从而使问题简化为一维问题。此外,我们还讨论了有界对称域,并提出了在这些域中证明伯恩斯-克兰茨刚性定理的方法,但这一方法并不适用于所有有界对称域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Holomorphic approximation by polynomials with exponents restricted to a convex cone The Denjoy-Wolff Theorem in simply connected domains Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean $L^2$-vanishing theorem and a conjecture of Kollár Nevanlinna Theory on Complete Kähler Connected Sums With Non-parabolic Ends
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1