ℂn的莱因哈特域B p n上的边界施瓦茨定理和刚性定理

IF 1.2 4区数学 Q1 MATHEMATICS Acta Mathematica Scientia Pub Date : 2024-05-01 DOI:10.1007/s10473-024-0304-y

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引用次数: 0

摘要

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。

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The boundary Schwarz lemma and the rigidity theorem on Reinhardt domains B p n of ℂn

Abstract

By introducing the Carathéodory metric, we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B _p ⁿ of ℂⁿ. Furthermore, the boundary rigidity theorem for holomorphic self-mappings defined on B _p ⁿ 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.

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来源期刊

Acta Mathematica Scientia 数学-数学

CiteScore

2.00

自引率

10.00%

发文量

2614

审稿时长

6 months

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.