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On the generalized squeezing functions and Fridman invariants of special domains

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Abstract

The main purpose of this paper is to study the generalized squeezing functions and Fridman invariants of some special domains. As applications, we give the precise form of generalized squeezing functions and Fridman invariants of various domains such as n-dimensional annuli. Furthermore, we provide domains with non-plurisubharmonic generalized squeezing function or Fridman invariant.

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References

  1. Ahlfors, L.V.: Complex Analysis. McGraw-Hill, New York (1979)

    MATH  Google Scholar 

  2. Alexander, H.: Extremal holomorphic imbeddings between the ball and polydisc. Proc. Amer. Math. Soc. 68, 200–202 (1978)

    Article  MathSciNet  Google Scholar 

  3. Arosio, L., Fornæss, J.E., Shcherbina, N., Wold, E.F.: Squeezing functions and Cantor sets. Ann. Sc. Norm. Super. Pisa Cl. Sci. 21(5), 1359–1369 (2020)

    MathSciNet  MATH  Google Scholar 

  4. Barth, T.J.: The Kobayashi indicatrix at the center of a circular domain. Proc. Amer. Math. Soc. 88, 527–530 (1983)

    Article  MathSciNet  Google Scholar 

  5. Deng, F., Guan, Q., Zhang, L.: Some properties of squeezing functions on bounded domains. Pacific J. Math. 257, 319–341 (2012)

    Article  MathSciNet  Google Scholar 

  6. Deng, F., Zhang, X.: Fridman's invariant, squeezing functions, and exhausting domains. Acta Math. Sin. (Engl. Ser.) 35, 1723–1728 (2019)

    Article  MathSciNet  Google Scholar 

  7. Deng, F., Wang, Z., Zhang, L., Zhou, X.: Holomorphic invariants of bounded domains. J. Geom. Anal. 30, 1204–1217 (2020)

    Article  MathSciNet  Google Scholar 

  8. Fornæss, J.E., Rong, F.: Estimate of the squeezing function for a class of bounded domains. Math. Ann. 371, 1087–1094 (2018)

    Article  MathSciNet  Google Scholar 

  9. Fridman, B.L.: On the imbedding of a strictly pseudoconvex domain in a polyhedron. Dokl. Akad. Nauk SSSR 249, 63–67 (1979) (Russian)

    MathSciNet  Google Scholar 

  10. Fridman, B.L.: Biholomorphic invariants of a hyperbolic manifold and some applications. Trans. Amer. Math. Soc. 276, 685–698 (1983)

    Article  MathSciNet  Google Scholar 

  11. Fornæss, J.E., Shcherbina, N.: A domain with non-plurisubharmonic squeezing function. J. Geom. Anal. 28, 13–21 (2018)

    Article  MathSciNet  Google Scholar 

  12. Joo, S., Kim, K.T.: On boundary points at which the squeezing function tends to one. J. Geom. Anal. 28, 2456–2465 (2018)

    Article  MathSciNet  Google Scholar 

  13. Jarnicki, M., Pflug, P.: Invariant Distances and Metrics in Complex Analysis. Walter de Gruyter, Basel (2013)

    Book  Google Scholar 

  14. Janardhanan, J.: Some results on holomorphic mappings of domains in \(\mathbb{C}^n\). Master’s thesis, Indian Institute of Science, (2009)

  15. Krantz, S.G.: Function Theory of Several Complex Variables. AMS Chelsea Publishing, Providence, RI (1992)

    MATH  Google Scholar 

  16. Kim, K.T., Zhang, L.: On the uniform squeezing property of bounded convex domains in \({\mathbb{C}}^n\). Pacific J. Math. 282, 341–358 (2016)

    Article  MathSciNet  Google Scholar 

  17. Lempert, L.: Holomorphic retracts and intrinsic metrics in convex domains. Anal. Math. 8, 257–261 (1982)

    Article  MathSciNet  Google Scholar 

  18. Mahajan, P., Verma, K.: A comparison of two biholomorphic invariants. Internat. J. Math. 30, 195–212 (2019)

    Article  MathSciNet  Google Scholar 

  19. Ng, T.W., Tang, C.C., Tsai, J.: The squeezing function on doubly-connected domains via the Loewner differential equation. Math. Ann. 380, 1741–1766 (2021)

    Article  MathSciNet  Google Scholar 

  20. Nikolov, N., Verma, K.: On the squeezing function and Fridman invariants. J. Geom. Anal. 30, 1218–1225 (2020)

    Article  MathSciNet  Google Scholar 

  21. Nikolov, N., Trybuła, M.: Estimates for the squeezing function near strictly pseudoconvex boundary points with applications. J. Geom. Anal. 30, 1359–1365 (2020)

    Article  MathSciNet  Google Scholar 

  22. Remmert, R., Stein, K.: Eigentliche holomorphe Abbildungen. Math. Z. 73, 159–189 (1960)

    Article  MathSciNet  Google Scholar 

  23. Rong, F., Yang, S.: On the comparison of the Fridman invariant and the squeezing function. Complex Var Ellip Equ (2020). https://doi.org/10.1080/17476933.2020.1851210

    Article  MATH  Google Scholar 

  24. Rong, F., Yang, S.: On Fridman invariants and generalized squeezing functions. Chin. Ann. Math. Ser. B. (to appear)

  25. Zhang, L.: Intrinsic derivative, curvature estimates and squeezing function. Sci. China Math. 60, 1149–1162 (2017)

    Article  MathSciNet  Google Scholar 

  26. Zimmer, A.: A gap theorem for the complex geometry of convex domains. Trans. Amer. Math. Soc. 370, 7489–7509 (2018)

    Article  MathSciNet  Google Scholar 

  27. Zimmer, A.: Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents. Math. Ann. 374, 1811–1844 (2019)

    Article  MathSciNet  Google Scholar 

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Funding

The authors are partially supported by the National Natural Science Foundation of China (grant no. 11871333).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai, 200240, People’s Republic of China

    Feng Rong

  2. School of Mathematics and Statistics, Huizhou University, 46 Yan Da Boulevard, Huizhou, Guangdong, 516007, People’s Republic of China

    Shichao Yang

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  1. Feng Rong
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  2. Shichao Yang
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Correspondence to Shichao Yang.

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Rong, F., Yang, S. On the generalized squeezing functions and Fridman invariants of special domains. Annali di Matematica 201, 1–15 (2022). https://doi.org/10.1007/s10231-021-01179-2

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  • DOI: https://doi.org/10.1007/s10231-021-01179-2

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