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Examples of hyperbolic spaces without the properties of quasi-ball or bounded eccentricity

Part of: Real and complex geometry Special aspects of infinite or finite groups

Published online by Cambridge University Press:  11 March 2024

Qizheng You  and
Jiawen Zhang
Qizheng You
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, China
Jiawen Zhang*
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai, 200433, China
*
Corresponding author: Jiawen Zhang; Email: jiawenzhang@fudan.edu.cn
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Abstract

In this note, we present examples of non-quasi-geodesic metric spaces which are hyperbolic (i.e., satisfying Gromov’s $4$-point condition) while the intersection of any two metric balls therein does not either ‘look like’ a ball or has uniformly bounded eccentricity. This answers an open question posed by Chatterji and Niblo.

Keywords

Gromov’s hyperbolic spacesNon-(quasi)-geodesicQuasi-ball propertyBounded eccentricity property

MSC classification

Primary: 51M09: Elementary problems in hyperbolic and elliptic geometries
Secondary: 20F67: Hyperbolic groups and nonpositively curved groups
Type
Research Article
Information
Glasgow Mathematical Journal , First View , pp. 1 - 9
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

†

JZ was partly supported by National Key R&D Program of China 2022YFA100700.

References

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