Abstract
A quantitative version of strong localization of the Kobayashi, Azukawa and Sibony metrics, as well as of the squeezing function, near a plurisubharmonic peak boundary point of a domain in \({\mathbb {C}}^n\) is given. As an application, the behavior of these metrics near a strictly pseudoconvex boundary point is studied. A weak localization of the three metrics and the squeezing function is also given near a plurisubharmonic antipeak boundary point.
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Notes
In fact, we need a weaker assumption on the respective antipeak function \(\varphi :\) \(\limsup _{z\rightarrow p}\varphi (z)<\inf _{D{\setminus } U}\varphi \) for any neighborhood U of p.
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Acknowledgements
The authors would like to thank the referee for his/her suggestion to consider a localization principle of invariant metrics at infinity.
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Communicated by Ngaiming Mok.
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Nikolai Nikolov was partially supported by the Bulgarian National Science Fund, Ministry of Education and Science of Bulgaria under contract DN 12/2. This paper was started while the first named author was visiting the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences in September 2019.
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Fornæss, J.E., Nikolov, N. Strong localization of invariant metrics. Math. Ann. 383, 353–360 (2022). https://doi.org/10.1007/s00208-021-02201-x
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DOI: https://doi.org/10.1007/s00208-021-02201-x