关于Kobayashi距离的域的局部和全局可见性和Gromov双曲性

IF 1.2 2区数学 Q1 MATHEMATICS

Transactions of the American Mathematical Society Pub Date : 2023-10-19 DOI:10.1090/tran/9010

Filippo Bracci, Hervé Gaussier, Nikolai Nikolov, Pascal Thomas

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引用次数: 0

摘要

在C d \mathbb {C}^d中引入了局部可见和局部Gromov双曲域的概念。我们证明了C d \mathbb {C}^d中的有界区域局部可见且局部Gromov双曲当且仅当它在Kobayashi距离上是(全局)可见且Gromov双曲。这允许从边界附近的局部信息中检测出那些是Gromov双曲的并且生物全纯态连续延伸到边界的域。

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Local and global visibility and Gromov hyperbolicity of domains with respect to the Kobayashi distance

We introduce the notion of locally visible and locally Gromov hyperbolic domains in C d \mathbb {C}^d . We prove that a bounded domain in C d \mathbb {C}^d is locally visible and locally Gromov hyperbolic if and only if it is (globally) visible and Gromov hyperbolic with respect to the Kobayashi distance. This allows to detect, from local information near the boundary, those domains which are Gromov hyperbolic and for which biholomorphisms extend continuously up to the boundary.

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来源期刊

Transactions of the American Mathematical Society 数学-数学

CiteScore

2.30

自引率

7.70%

发文量

171

审稿时长

3-6 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles in all areas of pure and applied mathematics. To be published in the Transactions, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Papers of less than 15 printed pages that meet the above criteria should be submitted to the Proceedings of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.