Abstract
In this paper, we study the link between the Angelo type of boundary point of bounded domain in \({\mathbb {C}}^d\) and the asymptotic behavior of the squeezing function corresponding to polydisk at that point. We restrict to the case \(d=2\) or convex domain.
Similar content being viewed by others
References
Berteloot, F.: Characterization of Models in \({\mathbb{C} }^2\) by their Automorphism groups. Int. J. Math. 5(5), 619–634 (1994)
Bracci, F., Gaussier, H., Zimmer, A.: The geometry of domains with negatively pinched Kähler metrics. arXiv:1810.11389 (2018)
Catlin, D.: Estimates of invariant metrics on pseudoconvex domains of dimension two. Math. Z. 200, 429–466 (1989)
Deng, F., Guan, Q., Zhang, L.: Properties of squeezing functions and global transformations of bounded domains. Trans. Am. Math. Soc. 368, 2679–2696 (2016)
Deng, F., Guan, Q., Zhang, L.: Some properties of squeezing functions on bounded domains. Pac. J. Math. 257(2), 319–341 (2012)
Fornaess, J.E.: The squeezing function. Talk at Bulgaria academy of science national mathematics colloqium (2019)
Gaussier, H.: On the gromov hyperbolicity of domains. Sémin. Théor. Spectr. Géom. Grenoble, 35, 23–42 (2017–2019)
Gaussier, H.: Characterization of convex domains with noncompact automorphism group. Michigan Math. J. 44(2), 375–388 (1997)
Greene, R.E., Krantz, S.G.: Biholomorphic self maps of domains. Lect. Notes Math. 1276, 153–319 (1990)
Gupta, N., Kumar, S.: Squeezing function corresponding to polydisk. arXiv:2007.14363 28 Jul 2020
Joo, S., Kim, K.T.: On boundary points at which the squeezing function tends to one. J. Geometr. Anal. (2016). https://doi.org/10.1007/s12220-017-9910-4
Kim, K.T., Zhang, L.: On the uniform squeezing property of bounded convex domains in \({\mathbb{C} }^n\). Pac. J. Math. 282(2), 341–358 (2016)
Kobayashi, S.: Hyperbolic complex spaces. In: Grundlehren der Mathematischen Wissenschaften, vol. 318. Springer, Berlin (1998)
Liu, K., Sun, X., Yau, S.T.: Canonical metrics on the moduli space of Riemann surfaces I. J. Differ. Geom. 68(3), 571–637 (2004)
Liu, K., Sun, X., Yau, S.T.: Canonical metrics on the moduli space of Riemann surfaces II. J. Differ. Geom. 69(1), 163–216 (2005)
Mahajan, P., Verma, K.: A comparison of two biholomorphic invariants. Int. J. Math. 30(1), 195–212 (2019)
Ng, T.W., Tang, C.C., Tsai, J.: The squeezing function on doubly-connected domains via the Loewner differential equation. Math. Ann. (2020). https://doi.org/10.1007/s00208-020-02046-w
Nikolov, N., Andreev, L.: Boundary behavior of the squeezing functions of \(C\)-convex domains and plane domains. Int. J. Math. 28, 5 (2017). https://doi.org/10.1142/S0129167X17500318
Yeung, S.K.: Geometry of domains with the uniform squeezing property. Adv. Math. 221(2), 547–569 (2009)
Zimmer, A.: A gap theorem for the complex geometry of convex domains. Trans. Am. Math. Soc. 370, 7489–7509 (2018)
Zimmer, A.: Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type. Math. Ann. 365, 1425–1498 (2016)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Guermazi, H., Haggui, F. On Some Properties of the Squeezing Function Corresponding to Polydisk. J Geom Anal 33, 28 (2023). https://doi.org/10.1007/s12220-022-01096-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12220-022-01096-7