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\(d\)-balanced squeezing function. (English) Zbl 1511.32009

Summary: We introduce the notion of \(d\)-balanced squeezing function motivated by the concept of generalized squeezing function given by Rong and Yang. In this work, we study some of its properties and its relation with the Fridman invariant.

MSC:

32F45 Invariant metrics and pseudodistances in several complex variables
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables

References:

[1] Rong, F, Yang, S. On Fridman invariants and generalized squeezing functions. Preprint (personal communication). · Zbl 1487.32082
[2] Gupta, N, Pant, SK. Squeezing function corresponding to polydisk, communicated; 2020. Available from: arXiv:2007.14363.
[3] Nikolov, N., The symmetrized polydisc cannot be exhausted by domains biholomorphic to convex domains, Ann Polon Math, 88, 279-283 (2006) · Zbl 1111.32020
[4] Ninh Van, T.; Nguyen Quang, D., Some properties of h-extendible domains in \(####\), J Math Anal Appl, 485, 2 (2020)
[5] Bharali, G. A new family of holomorphic homogeneous regular domains; 2021. Available from: arXiv:2103.09227.
[6] Jarnicki, M.; Pflug, P., Invariant distances and metrics in complex analysis (2013), Berlin: De Gruyter, Berlin · Zbl 1273.32002
[7] Lempert, L., Holomorphic retracts and intrinsic metrics in convex domains, Anal Math, 8, 257-261 (1982) · Zbl 0509.32015
[8] Kosinski, L.; Warszawski, T., Lempert theorem for strongly linearly convex domains, Ann Polon Math, 107, 2, 167-216 (2013) · Zbl 1268.32004
[9] Bharali, G. Non-isotropically balanced domains, Lempert function estimates, and the spectral Nevanlinna-Pick theorem; 2006. Available from: arXiv:0601107.
[10] Deng, F.; Guan, Q.; Zhang, L., Some properties of squeezing functions on bounded domains, Pacific J Math, 57, 2, 319-341 (2012) · Zbl 1254.32015
[11] Lloyd, NG., Remarks on generalising Rouché’s theorem, J London Math Soc (2), 20, 2, 259-272 (1979) · Zbl 0407.32002
[12] Jarnicki, M.; Pflug, P., First steps in several complex variables: Reinhardt domains (2008), Zürich: European Mathematical Society (EMS), Zürich · Zbl 1148.32001
[13] Deng, F.; Zhang, X., Fridman’s invariants squeezing functions and exhausting domains, Acta Math Sin (Engl Ser), 35, 1723-1728 (2019) · Zbl 1429.32023
[14] Nikolov, N.; Verma, K., On the squeezing function and Fridman invariants, J Geom Anal, 30, 1218-1225 (2019) · Zbl 1436.32048
[15] Rong, F.; Yang, S., On the comparison of the Fridman invariant and the squeezing function, Complex Var Elliptic Equ (2020) · Zbl 1487.32081 · doi:10.1080/17476933.2020.1851210
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