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A Remark on the Tautness modulo an Analytic Hypersurface of Hartogs-Type Domains

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Ukrainian Mathematical Journal Aims and scope

We present sufficient conditions for the tautness modulo an analytic hypersurface of Hartogs-type domains ΩH(X) and Hartogs–Laurent-type domains Σu,v(X). We also propose a version of Eastwood’s theorem for tautness modulo an analytic hypersurface.

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References

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

    Article  MathSciNet  Google Scholar 

  2. N. Q. Dieu and D. D. Thai, “Complete hyperbolicity of Hartogs domain,” Manuscripta Math., 112, 171–181 (2003).

    Article  MathSciNet  Google Scholar 

  3. P. V. Duc, N. T. Trang, and M. A. Duc, “On tautness modulo an analytic subset of complex spaces,” Acta Math. Vietnam, 42, 717–726 (2017).

    Article  MathSciNet  Google Scholar 

  4. A. Eastwood, “À propos des vari´et´es hyperboliques complétes,” C. R. Math. Acad. Sci. Paris, 280, 1071–1075 (1975).

    MathSciNet  MATH  Google Scholar 

  5. M. Jarnicki and P. Pflug, Invariant Distances and Metrics in Complex Analysis, de Gruyter, Berlin, New York (1993).

    Book  Google Scholar 

  6. S. Kobayashi, Hyperbolic Complex Spaces, Springer-Verlag, Berlin (1998).

    Book  Google Scholar 

  7. S. H. Park, “On hyperbolicity and tautness of certain Hartogs-type domains,” Rocky Mountain J. Math., 37, 959–985 (2007).

    Article  MathSciNet  Google Scholar 

  8. H. L. Royden, “Remark on the Kobayashi metric,” in: Several Complex Variables II Maryland. Lect. Notes Math., 185, Springer, Berlin, Heidelberg (1971), pp. 125–137.

    Google Scholar 

  9. D. D. Thai and Ph. V. Duc, “On the complete hyperbolicity and the tautness of the Hartogs domains,” Internat. J. Math., 11, 103–111 (2000).

    Article  MathSciNet  Google Scholar 

  10. D. D. Thai, M. A. Duc, and N. V. Thu, “On limit brody curves in ℂ2,” Kyushu J. Math., 69, No. 1, 111–123 (2015).

    Article  MathSciNet  Google Scholar 

  11. D. D. Thai and N. L. Huong, “A note on the Kobayashi pseudodistance and the tautness of holomorphic fiber bundles,” Ann. Polon. Math., 58, 1–5 (1980).

    MathSciNet  MATH  Google Scholar 

  12. D. D. Thai and J. Thomas, “D*-extension property without hyperbolicity,” Indiana Univ. Math. J., 47, 1125–1130 (1980).

    MathSciNet  MATH  Google Scholar 

  13. D. D. Thai, J. Thomas, N. V. Trao, and M. A. Duc, “On hyperbolicity and tautness modulo an analytic subset of Hartogs domains,” Proc. Amer. Math. Soc., 141, 3623–3631 (2013).

    Article  MathSciNet  Google Scholar 

  14. N. V. Trao and T. H. Minh, “Remarks on the Kobayashi hyperbolicity of complex spaces,” Acta Math. Vietnam, 34, 375–387 (2009).

    MathSciNet  MATH  Google Scholar 

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Correspondence to D. T. Pham.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 1, pp. 119–129, January, 2020.

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Pham, D.T. A Remark on the Tautness modulo an Analytic Hypersurface of Hartogs-Type Domains. Ukr Math J 72, 136–148 (2020). https://doi.org/10.1007/s11253-020-01767-0

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  • DOI: https://doi.org/10.1007/s11253-020-01767-0

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