两个度量的Gromov双曲性和强双曲性
Gromov Hyperbolicity and Strong Hyperbolicity of Two Metrics
DOI: 10.12677/PM.2023.1311335, PDF,   
作者: 徐 畅, 张孝惠：浙江理工大学理学院，浙江 杭州
关键词: Sign-型度量；Gromov双曲性；强双曲性；Sign-Like Metric； Gromov Hyperbolicity； Strong Hyperbolicity
摘要: 本文提出了在同一空间上的两个度量是sign-型的概念，研究了两个sign-型的Gromov双曲度量的和也具有Gromov双曲性，并推广至其线性组合的Gromov双曲性。在Ptolemy空间中，我们构造了一种强双曲度量。
Abstract: We introduce the notion of sign-likeness of two metrics on the same space, and study the Gromov hyperbolicity of the sum of two sign-like metrics which is generalized to the Gromov hyperbolicity of their linear combinations. In a Ptolemy space, we also construct a strongly hyperbolic metric.
文章引用：徐畅, 张孝惠. 两个度量的Gromov双曲性和强双曲性[J]. 理论数学, 2023, 13(11): 3219-3225. https://doi.org/10.12677/PM.2023.1311335

参考文献

[1] Gromov, M. (1987) Hyperbolic Groups. In: Gersten, S.M., Ed., Essays in Group Theory, Springer, New York, 75-263. [Google Scholar] [CrossRef] 
[2] Bonk, M., Heinonen, J. and Koskela, P. (2001) Uniformizing Gromov Hyperbolic Spaces. Asterisque Société Mathématique de France, Paris, 270.
[3] Buyalo, S. and Schroeder, V. (2007) Elements of Asymptotic Geometry. EMS Press, Berlin. [Google Scholar] [CrossRef] 
[4] Väisälä, J. (2005) Gromov Hyperbolic Spaces. Expositiones Mathematicae, 23, 187-231. [Google Scholar] [CrossRef] 
[5] Gehring, F.W. and Osgood, B.G. (1979) Uniform Domains and the Quasihyperbolic Metric. Journal d’Analyse Mathématique, 36, 50-74. [Google Scholar] [CrossRef] 
[6] Ibragimov, Z. (2009) The Cassinian Metric of a Domain in Rn. Uzbek Mathematical Journal, 1, 53-67.
[7] Chen, J., Hariri, P., Klén, R. and Vuorinen, M. (2015) Lipschitz Conditions, Triangular Ratio Metric, and Quasiconformal Maps. Annales Academiae Scientiarum Fennicae-Mathematica, 40, 683-709. [Google Scholar] [CrossRef] 
[8] Ibragimov, Z. (2011) Hyperbolizing Metric Spaces. Proceedings of the American Mathematical Society, 139, 4401-4407. [Google Scholar] [CrossRef] 
[9] Aksoy, A., Ibragimov, Z. and Whiting, W. (2018) Av-eraging One-Point Hyperbolic-Type Metrics. Proceedings of the American Mathematical Society, 146, 5205-5218. [Google Scholar] [CrossRef] 
[10] Nica, B. and Špakula, J. (2016) Strong Hyperbolicity. Groups Geometry and Dynamics, 10, 951-964. [Google Scholar] [CrossRef] 
[11] Zhang, Z. and Xiao, Y. (2019) Strongly Hyperbolic Metrics on Ptolemy Spaces. Journal of Mathematical Analysis and Applications, 478, 445-457. [Google Scholar] [CrossRef] 
[12] Katz, N.N. (2021) Hyperbolic Metrics on Open Subsets of Ptol-emaic Spaces with Sharp Parameter Bounds. Proceedings of the American Mathematical Society, 149, 2213-2220. [Google Scholar] [CrossRef] 

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