Abstract
In the present article, we define squeezing function corresponding to polydisk and study its properties. We investigate relationship between squeezing function and squeezing function corresponding to polydisk.
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Alexander, H.: Extremal holomorphic imbeddings between the ball and polydisc. Proc. Am. Math. Soc. 68(2), 200–202 (1978)
Barth, T.J.: The Kobayashi distance induces the standard topology. Proc. Am. Math. Soc. 35(2), 439–441 (1972)
Deng, F., Guan, Q., Zhang, L.: Some properties of squeezing functions on bounded domains. Pac. J. Math. 57(2), 319–342 (2012)
Deng, F., Zhang, X.: Fridman’s invariants, squeezing functions and exhausting domains. Acta Math. Sin. (Engl. Ser.) 35, 1723–1728 (2019)
Deng, F., Guan, Q., Zhang, L.: Properties of squeezing functions and global transformations of bounded domains. Trans. Am. Math. Soc. 368, 2679–2696 (2016)
Fornæss, J.E.: The squeezing function, Talk at Bulgaria academy of science national mathematics colloquium (2019)
Fridman, B.L.: On the imbedding of a strictly pseudoconvex domain in a polyhedron. Dokl. Akad. Nauk SSSR 249(1), 63–67 (1979)
Fridman, B.L.: Biholomorphic invariants of a hyperbolic manifold and some applications. Trans. Am. Math. Soc. 276, 685–698 (1983)
Joo, S., Kim, K.T.: On boundary points at which the squeezing function tends to one. J. Geom. 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)
Kubota, Y.: An extremal problem on the classical Cartan domain II. Kodai Math. J. 5, 218–224 (1982)
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)
Lloyd, N.G.: Remarks on generalising Rouche’s theorem. J. Lond. Math. Soc. 2(20), 259–272 (1979)
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. (2017). https://doi.org/10.1142/S0129167X17500318
Nikolov, N., Verma, K.: On the squeezing function and Fridman invariants. J. Geom. Anal. 30, 1218–1225 (2019)
Rudin, W.: Function Theory in Polydiscs. Springer, New York (1980)
Rudin, W.: Function Theory in the Unit Ball of \({\mathbb{C}}^n\). Springer, Berlin (1980)
Steven, G., Krantz: Function Theory of Several Complex Variables. AMS Chelsea Publishing, Providence (1992)
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)
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We thank Gautam Bharali for his critical and valuable insights for improving the article. We profusely thank the referee for several valuable comments and suggestions.
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Gupta, N., Pant, S.K. Squeezing function corresponding to polydisk. Complex Anal Synerg 8, 12 (2022). https://doi.org/10.1007/s40627-022-00100-8
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DOI: https://doi.org/10.1007/s40627-022-00100-8