LOCAL AND GLOBAL VISIBILITY AND GROMOV HYPERBOLICITY OF DOMAINS WITH RESPECT TO THE KOBAYASHI DISTANCE

被引：0

作者：

Bracci, Filippo ^{[1
]}

Gaussier, Herve ^{[2
,3
]}

Nikolov, Nikolai ^{[4
,5
]}

Thomas, Pascal J. ^{[6
,7
]}

机构：

[1] Univ Roma Tor Vergata, Dipartimento Matemat, Via Ric Scientif 1, I-00133 Rome, Italy

[2] Univ Grenoble Alpes, IF, F-38000 Grenoble, France

[3] CNRS, IF, F-38000 Grenoble, France

[4] Bulgarian Acad Sci, Inst Math & Informat, Acad G Bonchev Str,Block 8, Sofia 1113, Bulgaria

[5] State Univ Lib Studies & Informat Technol, Fac Informat Sci, 69A,Shipchenskiprohod Str, Sofia 1574, Bulgaria

[6] Univ Toulouse, Inst Math Toulouse, UMR 5219, F-31062 Toulouse 9, France

[7] CNRS, UPS, F-31062 Toulouse 9, France

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2024年 / 377卷 / 01期

关键词：

Gromov hyperbolic spaces; Kobayashi hyperbolic spaces; visibility; extension of holomorphic maps; localization; WEAK NOTION;

D O I：

10.1090/tran/9010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the notion of locally visible and locally Gromov hyperbolic domains in C-d. We prove that a bounded domain in 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.

引用

页码：471 / 493

页数：23

共 8 条

[1] Local and global notions of visibility with respect to Kobayashi distance: a comparison
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ANNALES POLONICI MATHEMATICI, 2024, 132 (02) : 169 - 185
[2] Notions of visibility with respect to the Kobayashi distance: comparison and applications
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[3] Notions of visibility with respect to the Kobayashi distance: comparison and applications
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[4] Localization of the Kobayashi Distance for any Visibility Domain
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[5] Localization of the Kobayashi Distance for any Visibility Domain
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The Journal of Geometric Analysis, 2023, 33
[6] Visibility of Kobayashi geodesics in convex domains and related properties
Bracci, Filippo
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Thomas, Pascal J.
MATHEMATISCHE ZEITSCHRIFT, 2022, 301 (02) : 2011 - 2035
[7] Visibility of Kobayashi geodesics in convex domains and related properties
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Nikolai Nikolov
Pascal J. Thomas
Mathematische Zeitschrift, 2022, 301 : 2011 - 2035
[8] A study of global and local visibility as web indicators of research production
Martinez-Torres, M. R.
Diaz-Fernandez, M. C.
RESEARCH EVALUATION, 2013, 22 (03) : 157 - 168

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