Holomorphic isometric maps from the complex unit ball to reducible bounded symmetric domains

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-06-25 DOI:10.1515/crelle-2022-0029

Ming Xiao

引用次数: 0

Abstract

Abstract The first part of the paper studies the boundary behavior of holomorphic isometric mappings F=(F1,…,Fm){F=(F_{1},\dots,F_{m})} from the complex unit ball 𝔹n{\mathbb{B}^{n}}, n≥2{n\geq 2}, to a bounded symmetric domain Ω=Ω1×⋯×Ωm{\Omega=\Omega_{1}\times\cdots\times\Omega_{m}} up to constant conformal factors, where Ωi′{\Omega_{i}^{\prime}}s are irreducible factors of Ω. We prove every non-constant component Fi{F_{i}} must map generic boundary points of 𝔹n{\mathbb{B}^{n}} to the boundary of Ωi{\Omega_{i}}. In the second part of the paper, we establish a rigidity result for local holomorphic isometric maps from the unit ball to a product of unit balls and Lie balls.

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复单位球到可约有界对称区域的全纯等距映射

摘要本文第一部分研究了全纯等距映射F=(F1，…，Fm){F=(F＿1{, }\dots,{F＿m})}从复单位球𝔹n {\mathbb{B} ^n{, }}n{≥2n\geq 2}到有界对称域Ω=Ω1×⋯×Ωm{\Omega = \Omega ＿1{}\times\cdots\times\Omega ＿m{直至常数保形因子，其中Ωi ' }}{\Omega ＿i{^ }{\prime}} s是Ω的不可约因子。证明了每个非常数分量{FiF＿i{必须}}映射𝔹n {\mathbb{B} ^n的一般{边界}}点到Ωi {\Omega ＿i的边界。在论文的第二{部分}}，我们建立了从单位球到单位球与李球积的局部全纯等距映射的刚性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.